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Wajib.","2026-10-08T09:24:41.433Z",{"id":290,"subjectId":14,"levelId":48,"parentId":91,"slug":1448,"name":1449,"description":1450,"order":1451,"createdAt":1452,"updatedAt":1452},"matriks","Matriks","Matriks — Kelas 11 Lanjut.",13,"2026-10-08T09:24:41.441Z",{"id":1454,"subjectId":23,"levelId":48,"parentId":91,"slug":1455,"name":1456,"description":1457,"order":1451,"createdAt":1458,"updatedAt":1458},"cmuzbyhhz003k71r9s7s8evk1","rangkaian-pegas","Rangkaian Pegas","Rangkaian Pegas — Kelas 11.","2026-10-08T09:24:41.111Z",{"id":152,"subjectId":23,"levelId":48,"parentId":91,"slug":1460,"name":1461,"description":1462,"order":1463,"createdAt":1464,"updatedAt":1464},"fluida","Fluida","Fluida — Kelas 11.",14,"2026-10-08T09:24:41.113Z",{"id":266,"subjectId":14,"levelId":48,"parentId":91,"slug":1466,"name":1467,"description":1468,"order":1463,"createdAt":1469,"updatedAt":1469},"polinomial","Polinomial","Polinomial — Kelas 11 Lanjut.","2026-10-08T09:24:41.454Z",{"id":182,"subjectId":14,"levelId":48,"parentId":91,"slug":1471,"name":1472,"description":1473,"order":1474,"createdAt":1475,"updatedAt":1475},"fungsi-trigonometri","Fungsi Trigonometri","Fungsi Trigonometri — Kelas 11 Lanjut.",15,"2026-10-08T09:24:41.469Z",{"id":176,"subjectId":23,"levelId":48,"parentId":91,"slug":1477,"name":1478,"description":1479,"order":1474,"createdAt":1480,"updatedAt":1480},"gerak-harmonik-sederhana-ghs","Gerak Harmonik Sederhana (GHS)","Gerak Harmonik Sederhana (GHS) — Kelas 11.","2026-10-08T09:24:41.119Z",{"id":206,"subjectId":23,"levelId":48,"parentId":91,"slug":1482,"name":1483,"description":1484,"order":1485,"createdAt":1486,"updatedAt":1486},"gelombang-mekanik","Gelombang Mekanik","Gelombang Mekanik — Kelas 11.",16,"2026-10-08T09:24:41.132Z",{"id":272,"subjectId":14,"levelId":48,"parentId":91,"slug":1241,"name":1242,"description":1488,"order":1485,"createdAt":1489,"updatedAt":1489},"Vektor — Kelas 11 Lanjut.","2026-10-08T09:24:41.485Z",{"id":128,"subjectId":23,"levelId":48,"parentId":91,"slug":1491,"name":1492,"description":1493,"order":1494,"createdAt":1495,"updatedAt":1495},"gelombang-cahaya","Gelombang Cahaya","Gelombang Cahaya — Kelas 11.",17,"2026-10-08T09:24:41.150Z",{"id":212,"subjectId":14,"levelId":48,"parentId":91,"slug":1497,"name":1498,"description":1499,"order":1494,"createdAt":1500,"updatedAt":1500},"transformasi-geometri","Transformasi Geometri","Transformasi Geometri — Kelas 11 Lanjut.","2026-10-08T09:24:41.498Z",{"id":158,"subjectId":14,"levelId":48,"parentId":91,"slug":1502,"name":1503,"description":1504,"order":1505,"createdAt":1506,"updatedAt":1506},"fungsi-dan-pemodelannya","Fungsi dan Pemodelannya","Fungsi dan Pemodelannya — Kelas 11 Lanjut.",18,"2026-10-08T09:24:41.504Z",{"id":194,"subjectId":23,"levelId":48,"parentId":91,"slug":1508,"name":1509,"description":1510,"order":1505,"createdAt":1511,"updatedAt":1511},"optik","Optik","Optik — Kelas 11.","2026-10-08T09:24:41.161Z",{"id":68,"subjectId":14,"levelId":48,"parentId":91,"slug":1513,"name":76,"description":1514,"order":1515,"createdAt":1516,"updatedAt":1516},"barisan-dan-deret-kelas-12-wajib","Barisan dan Deret — Kelas 12 Wajib.",19,"2026-10-08T09:24:41.512Z",{"id":367,"subjectId":23,"levelId":48,"parentId":91,"slug":1518,"name":1519,"description":1520,"order":1515,"createdAt":1521,"updatedAt":1521},"suhu-dan-kalor","Suhu dan Kalor","Suhu dan Kalor — Kelas 11.","2026-10-08T09:24:41.169Z",{"id":98,"subjectId":14,"levelId":48,"parentId":91,"slug":1523,"name":1524,"description":1525,"order":1526,"createdAt":1527,"updatedAt":1527},"bunga","Bunga","Bunga — Kelas 12 Wajib.",20,"2026-10-08T09:24:41.518Z",{"id":164,"subjectId":23,"levelId":48,"parentId":91,"slug":1529,"name":1530,"description":1531,"order":1526,"createdAt":1532,"updatedAt":1532},"teori-kinetik-gas","Teori Kinetik Gas","Teori Kinetik Gas — Kelas 11.","2026-10-08T09:24:41.188Z",{"id":373,"subjectId":14,"levelId":48,"parentId":91,"slug":1534,"name":1535,"description":1536,"order":1537,"createdAt":1538,"updatedAt":1538},"investasi-dan-pinjaman","Investasi dan Pinjaman","Investasi dan Pinjaman — Kelas 12 Wajib.",21,"2026-10-08T09:24:41.525Z",{"id":391,"subjectId":23,"levelId":48,"parentId":91,"slug":1540,"name":1541,"description":1542,"order":1537,"createdAt":1543,"updatedAt":1543},"termodinamika","Termodinamika","Termodinamika — Kelas 11.","2026-10-08T09:24:41.202Z",{"id":319,"subjectId":14,"levelId":48,"parentId":91,"slug":1545,"name":1546,"description":1547,"order":1548,"createdAt":1549,"updatedAt":1549},"kaidah-pencacahan","Kaidah Pencacahan","Kaidah Pencacahan — Kelas 12 Wajib.",22,"2026-10-08T09:24:41.540Z",{"id":260,"subjectId":23,"levelId":48,"parentId":91,"slug":1551,"name":1552,"description":1553,"order":1548,"createdAt":1554,"updatedAt":1554},"listrik-statis","Listrik Statis","Listrik Statis — Kelas 12.","2026-10-08T09:24:41.215Z",{"id":230,"subjectId":23,"levelId":48,"parentId":91,"slug":1556,"name":1557,"description":1558,"order":1559,"createdAt":1560,"updatedAt":1560},"listrik-arus-searah","Listrik Arus Searah","Listrik Arus Searah — Kelas 12.",23,"2026-10-08T09:24:41.227Z",{"id":278,"subjectId":14,"levelId":48,"parentId":91,"slug":1562,"name":1411,"description":1563,"order":1559,"createdAt":1564,"updatedAt":1564},"peluang-kelas-12-wajib","Peluang — Kelas 12 Wajib.","2026-10-08T09:24:41.547Z",{"id":242,"subjectId":14,"levelId":48,"parentId":91,"slug":1566,"name":1567,"description":1568,"order":1569,"createdAt":1570,"updatedAt":1570},"geometri-analitik","Geometri Analitik","Geometri Analitik — Kelas 12 Lanjut.",24,"2026-10-08T09:24:41.553Z",{"id":236,"subjectId":23,"levelId":48,"parentId":91,"slug":1572,"name":1573,"description":1574,"order":1569,"createdAt":1575,"updatedAt":1575},"kemagnetan","Kemagnetan","Kemagnetan — Kelas 12.","2026-10-08T09:24:41.245Z",{"id":110,"subjectId":14,"levelId":48,"parentId":91,"slug":1577,"name":1578,"description":1579,"order":1580,"createdAt":1581,"updatedAt":1581},"limit","Limit","Limit — Kelas 12 Lanjut.",25,"2026-10-08T09:24:41.562Z",{"id":61,"subjectId":23,"levelId":48,"parentId":91,"slug":1583,"name":1584,"description":1585,"order":1580,"createdAt":1586,"updatedAt":1586},"listrik-ac-arus-bolak-balik","Listrik AC \u002F Arus Bolak Balik","Listrik AC \u002F Arus Bolak Balik — Kelas 12.","2026-10-08T09:24:41.263Z",{"id":301,"subjectId":23,"levelId":48,"parentId":91,"slug":1588,"name":1589,"description":1590,"order":1591,"createdAt":1592,"updatedAt":1592},"gelombang-elektromagnetik","Gelombang Elektromagnetik","Gelombang Elektromagnetik — Kelas 12.",26,"2026-10-08T09:24:41.273Z",{"id":116,"subjectId":14,"levelId":48,"parentId":91,"slug":1594,"name":1595,"description":1596,"order":1591,"createdAt":1597,"updatedAt":1597},"turunan-fungsi","Turunan Fungsi","Turunan Fungsi — Kelas 12 Lanjut.","2026-10-08T09:24:41.575Z",{"id":325,"subjectId":14,"levelId":48,"parentId":91,"slug":1599,"name":1600,"description":1601,"order":1602,"createdAt":1603,"updatedAt":1603},"aplikasi-turunan","Aplikasi Turunan","Aplikasi Turunan — Kelas 12 Lanjut.",27,"2026-10-08T09:24:41.587Z",{"id":355,"subjectId":23,"levelId":48,"parentId":91,"slug":1605,"name":1606,"description":1607,"order":1602,"createdAt":1608,"updatedAt":1608},"pengantar-instrumental-digital","Pengantar Instrumental Digital","Pengantar Instrumental Digital — Kelas 12.","2026-10-08T09:24:41.283Z",{"id":200,"subjectId":14,"levelId":48,"parentId":91,"slug":1610,"name":1611,"description":1612,"order":1613,"createdAt":1614,"updatedAt":1614},"integral","Integral","Integral — Kelas 12 Lanjut.",28,"2026-10-08T09:24:41.599Z",{"id":343,"subjectId":23,"levelId":48,"parentId":91,"slug":1616,"name":1617,"description":1618,"order":1613,"createdAt":1619,"updatedAt":1619},"relativitas-khusus","Relativitas Khusus","Relativitas Khusus — Kelas 12.","2026-10-08T09:24:41.291Z",{"id":349,"subjectId":23,"levelId":48,"parentId":91,"slug":1621,"name":1622,"description":1623,"order":1624,"createdAt":1625,"updatedAt":1625},"gejala-kuantum","Gejala Kuantum","Gejala Kuantum — Kelas 12.",29,"2026-10-08T09:24:41.303Z",{"id":248,"subjectId":14,"levelId":48,"parentId":91,"slug":1627,"name":1628,"description":1629,"order":1624,"createdAt":1630,"updatedAt":1630},"penerapan-integral","Penerapan Integral","Penerapan Integral — Kelas 12 Lanjut.","2026-10-08T09:24:41.607Z",{"id":140,"subjectId":14,"levelId":48,"parentId":91,"slug":1632,"name":1633,"description":1634,"order":1635,"createdAt":1636,"updatedAt":1636},"analisis-data-peluang","Analisis Data & Peluang","Analisis Data & Peluang — Kelas 12 Lanjut.",30,"2026-10-08T09:24:41.611Z",{"id":284,"subjectId":23,"levelId":48,"parentId":91,"slug":1638,"name":1639,"description":1640,"order":1635,"createdAt":1641,"updatedAt":1641},"fisika-inti-dan-radioaktivitas","Fisika Inti dan Radioaktivitas","Fisika Inti dan Radioaktivitas — Kelas 12.","2026-10-08T09:24:41.318Z",{"id":1643,"subjectId":14,"levelId":48,"parentId":91,"slug":1644,"name":1645,"description":1646,"order":1647,"createdAt":1648,"updatedAt":1648},"cmuzbyhw700gw71r9o87lq7vd","logaritma","Logaritma","Logaritma — Kelas 12 Lanjut.",31,"2026-10-08T09:24:41.623Z",{"id":1650,"subjectId":14,"levelId":48,"parentId":91,"slug":1651,"name":1652,"description":1653,"order":1654,"createdAt":1655,"updatedAt":1655},"cmuzbyhw900gy71r9d9sjh9ie","program-linier","Program Linier","Program Linier — Kelas 12 Lanjut.",32,"2026-10-08T09:24:41.625Z",{"id":1657,"subjectId":14,"levelId":48,"parentId":91,"slug":1658,"name":1659,"description":1660,"order":1661,"createdAt":1662,"updatedAt":1662},"cmuzbyhwb00h071r97764r7hr","bangun-ruang","Bangun Ruang","Bangun Ruang — Kelas 12 Lanjut.",33,"2026-10-08T09:24:41.627Z",{"id":1664,"subjectId":32,"levelId":91,"parentId":91,"slug":1665,"name":1666,"description":1667,"order":1668,"createdAt":1669,"updatedAt":1669},"demo-v2-topic-pemrograman-sd-1","demo-v2-sd-1","Algoritma: Urutan Perintah yang Jelas","Susun instruksi sederhana, lalu telusuri hasilnya selangkah demi selangkah.",100,"2026-10-08T10:03:56.954Z",{"id":1671,"subjectId":14,"levelId":48,"parentId":91,"slug":1672,"name":1673,"description":1674,"order":1668,"createdAt":1675,"updatedAt":1675},"demo-v2-topic-matematika-sma-1","demo-v2-sma-1","Fungsi kuadrat: akar, puncak, dan bentuk grafik","Menghubungkan bentuk umum, faktor, dan kuadrat sempurna untuk memahami parabola dan nilai optimum.","2026-10-08T10:03:56.485Z",{"id":1677,"subjectId":32,"levelId":48,"parentId":91,"slug":1672,"name":1678,"description":1679,"order":1668,"createdAt":1680,"updatedAt":1680},"demo-v2-topic-pemrograman-sma-1","Fungsi: Memisahkan Masukan, Proses, dan Hasil","Buat fungsi Python yang bisa dipakai ulang dan bedakan return dari print.","2026-10-08T10:03:57.108Z",{"id":1682,"subjectId":23,"levelId":42,"parentId":91,"slug":1683,"name":1684,"description":1685,"order":1668,"createdAt":1686,"updatedAt":1686},"demo-v2-topic-fisika-smp-1","demo-v2-smp-1","Gerak Lurus: Jarak, Perpindahan, dan Grafik Posisi","Membedakan kelajuan dan kecepatan rata-rata serta membaca arti kemiringan grafik posisi terhadap waktu.","2026-10-08T10:03:56.729Z",{"id":1688,"subjectId":23,"levelId":48,"parentId":91,"slug":1672,"name":1689,"description":1690,"order":1668,"createdAt":1691,"updatedAt":1691},"demo-v2-topic-fisika-sma-1","Hukum II Newton dan Gesekan pada Bidang Datar","Membuat diagram gaya, menentukan resultan, dan membedakan gesekan statis dari gesekan kinetik.","2026-10-08T10:03:56.801Z",{"id":1693,"subjectId":23,"levelId":91,"parentId":91,"slug":1665,"name":1694,"description":1695,"order":1668,"createdAt":1696,"updatedAt":1696},"demo-v2-topic-fisika-sd-1","Mengukur Panjang dan Volume Benda","Membaca penggaris, memakai satuan baku, dan menghitung isi kubus melalui susunan kubus kecil.","2026-10-08T10:03:56.657Z",{"id":1698,"subjectId":32,"levelId":53,"parentId":91,"slug":1699,"name":1700,"description":1701,"order":1668,"createdAt":1702,"updatedAt":1702},"demo-v2-topic-pemrograman-kuliah-1","demo-v2-kuliah-1","Pencarian Linear, Set, dan Biaya Operasi","Bandingkan cara mencari anggota data melalui langkah yang benar-benar dikerjakan.","2026-10-08T10:03:57.182Z",{"id":1704,"subjectId":14,"levelId":42,"parentId":91,"slug":1683,"name":1705,"description":1706,"order":1668,"createdAt":1707,"updatedAt":1707},"demo-v2-topic-matematika-smp-1","Perbandingan senilai dan berbalik nilai","Memilih model dari besaran yang tetap: rasio tetap untuk senilai dan hasil kali tetap untuk berbalik nilai.","2026-10-08T10:03:56.412Z",{"id":1709,"subjectId":14,"levelId":53,"parentId":91,"slug":1699,"name":1710,"description":1711,"order":1668,"createdAt":1712,"updatedAt":1712},"demo-v2-topic-matematika-kuliah-1","Turunan sebagai laju sesaat dan pendekatan lokal","Menurunkan fungsi dari limit hasil bagi selisih serta menghubungkan kemiringan, kecepatan, dan garis singgung.","2026-10-08T10:03:56.556Z",{"id":1714,"subjectId":32,"levelId":42,"parentId":91,"slug":1683,"name":1715,"description":1716,"order":1668,"createdAt":1717,"updatedAt":1717},"demo-v2-topic-pemrograman-smp-1","Variabel, Tipe Data, dan Keluaran Python","Simpan nilai dengan nama yang jelas dan bedakan angka dari teks.","2026-10-08T10:03:57.035Z",{"id":1719,"subjectId":23,"levelId":53,"parentId":91,"slug":1699,"name":1720,"description":1721,"order":1668,"createdAt":1722,"updatedAt":1722},"demo-v2-topic-fisika-kuliah-1","Vektor Tiga Dimensi dan Usaha sebagai Hasil Kali Titik","Menghubungkan komponen, panjang vektor, vektor satuan, proyeksi, dan makna fisik hasil kali titik.","2026-10-08T10:03:56.874Z",{"id":1724,"subjectId":14,"levelId":48,"parentId":91,"slug":1725,"name":1726,"description":1727,"order":1728,"createdAt":1729,"updatedAt":1729},"demo-v2-topic-matematika-sma-2","demo-v2-sma-2","Eksponen dan logaritma: mencari pangkat yang belum diketahui","Membedakan kenaikan tetap dan faktor tetap, lalu membaca logaritma sebagai operasi balik eksponen.",101,"2026-10-08T10:03:56.507Z",{"id":1731,"subjectId":14,"levelId":42,"parentId":91,"slug":1732,"name":1733,"description":1734,"order":1728,"createdAt":1735,"updatedAt":1735},"demo-v2-topic-matematika-smp-2","demo-v2-smp-2","Fungsi linear: gradien dan titik potong","Membaca y = mx + b sebagai perubahan tetap, menghitung gradien dari dua titik, dan memeriksa grafik.","2026-10-08T10:03:56.434Z",{"id":1737,"subjectId":23,"levelId":91,"parentId":91,"slug":1738,"name":1739,"description":1740,"order":1728,"createdAt":1741,"updatedAt":1741},"demo-v2-topic-fisika-sd-2","demo-v2-sd-2","Gaya: Dorongan, Tarikan, dan Perubahan Gerak","Mengenali siapa yang memberikan gaya, arah gaya, dan perubahan gerak atau bentuk yang dapat diamati.","2026-10-08T10:03:56.679Z",{"id":1743,"subjectId":23,"levelId":48,"parentId":91,"slug":1725,"name":1744,"description":1745,"order":1728,"createdAt":1746,"updatedAt":1746},"demo-v2-topic-fisika-sma-2","Gerak Peluru: Dua Arah dengan Satu Waktu","Menguraikan kecepatan awal, menghitung waktu terbang, tinggi maksimum, dan jangkauan untuk model ideal.","2026-10-08T10:03:56.824Z",{"id":1748,"subjectId":14,"levelId":53,"parentId":91,"slug":1749,"name":1750,"description":1751,"order":1728,"createdAt":1752,"updatedAt":1752},"demo-v2-topic-matematika-kuliah-2","demo-v2-kuliah-2","Integral tentu: akumulasi dan luas bertanda","Menghubungkan jumlah Riemann, antiturunan, dan teorema dasar kalkulus tanpa menyamakan perpindahan dengan jarak.","2026-10-08T10:03:56.578Z",{"id":1754,"subjectId":32,"levelId":53,"parentId":91,"slug":1749,"name":1755,"description":1756,"order":1728,"createdAt":1757,"updatedAt":1757},"demo-v2-topic-pemrograman-kuliah-2","Kelas dan Invarian pada Objek","Kelola keadaan dan perilaku bersama, lalu jaga agar objek selalu valid.","2026-10-08T10:03:57.206Z",{"id":1759,"subjectId":32,"levelId":48,"parentId":91,"slug":1725,"name":1760,"description":1761,"order":1728,"createdAt":1762,"updatedAt":1762},"demo-v2-topic-pemrograman-sma-2","List dan Dictionary untuk Mengolah Data","Pilih struktur data sesuai cara mengaksesnya dan hitung ringkasan data.","2026-10-08T10:03:57.131Z",{"id":1764,"subjectId":23,"levelId":42,"parentId":91,"slug":1732,"name":1765,"description":1766,"order":1728,"createdAt":1767,"updatedAt":1767},"demo-v2-topic-fisika-smp-2","Massa Jenis: Menghubungkan Massa dan Volume","Menghitung massa jenis, mengukur volume dengan perpindahan air, dan menjaga konsistensi satuan.","2026-10-08T10:03:56.750Z",{"id":1769,"subjectId":23,"levelId":53,"parentId":91,"slug":1749,"name":1770,"description":1771,"order":1728,"createdAt":1772,"updatedAt":1772},"demo-v2-topic-fisika-kuliah-2","Osilasi Harmonik Sederhana: Fase, Turunan, dan Energi","Menganalisis model x = A cos(ωt), menurunkan kecepatan dan percepatan, serta memeriksa kekekalan energi.","2026-10-08T10:03:56.896Z",{"id":1774,"subjectId":32,"levelId":91,"parentId":91,"slug":1738,"name":1775,"description":1776,"order":1728,"createdAt":1777,"updatedAt":1777},"demo-v2-topic-pemrograman-sd-2","Pengulangan: Langkah yang Dikerjakan Berkali-kali","Kenali pola berulang dan hitung hasil tiap putaran tanpa kehilangan jejak.","2026-10-08T10:03:56.978Z",{"id":1779,"subjectId":32,"levelId":42,"parentId":91,"slug":1732,"name":1780,"description":1781,"order":1728,"createdAt":1782,"updatedAt":1782},"demo-v2-topic-pemrograman-smp-2","Percabangan Python dan Batas Keputusan","Tulis if, elif, dan else serta uji nilai di sekitar batas.","2026-10-08T10:03:57.057Z",{"id":1784,"subjectId":23,"levelId":48,"parentId":91,"slug":1785,"name":1786,"description":1787,"order":1788,"createdAt":1789,"updatedAt":1789},"demo-v2-topic-fisika-sma-3","demo-v2-sma-3","Hukum Ohm, Daya, dan Energi pada Resistor","Menghubungkan tegangan, arus, hambatan, dan energi listrik tanpa mencampurkan satuan volt, ampere, watt, dan joule.",102,"2026-10-08T10:03:56.846Z",{"id":1791,"subjectId":32,"levelId":48,"parentId":91,"slug":1785,"name":1792,"description":1793,"order":1788,"createdAt":1794,"updatedAt":1794},"demo-v2-topic-pemrograman-sma-3","Membaca Berkas dan Menangani Masukan Salah","Ubah baris teks menjadi angka dan tangani kesalahan yang bisa diperkirakan.","2026-10-08T10:03:57.153Z",{"id":1796,"subjectId":14,"levelId":48,"parentId":91,"slug":1785,"name":1797,"description":1798,"order":1788,"createdAt":1799,"updatedAt":1799},"demo-v2-topic-matematika-sma-3","Peluang: ruang sampel, kejadian, dan pengambilan bertahap","Menghitung peluang melalui hasil yang sama mungkin dan memahami pengaruh pengembalian pada pengambilan kedua.","2026-10-08T10:03:56.528Z",{"id":1801,"subjectId":32,"levelId":53,"parentId":91,"slug":1802,"name":1803,"description":1804,"order":1788,"createdAt":1805,"updatedAt":1805},"demo-v2-topic-pemrograman-kuliah-3","demo-v2-kuliah-3","Pengujian Otomatis dan Kasus Batas","Uji kontrak fungsi dengan contoh biasa, batas, dan masukan tidak sah.","2026-10-08T10:03:57.229Z",{"id":1807,"subjectId":32,"levelId":91,"parentId":91,"slug":1808,"name":1809,"description":1810,"order":1788,"createdAt":1811,"updatedAt":1811},"demo-v2-topic-pemrograman-sd-3","demo-v2-sd-3","Percabangan: Memilih Tindakan dengan Syarat","Gunakan pertanyaan ya atau tidak untuk menentukan tindakan yang tepat.","2026-10-08T10:03:57.006Z",{"id":1813,"subjectId":32,"levelId":42,"parentId":91,"slug":1814,"name":1815,"description":1816,"order":1788,"createdAt":1817,"updatedAt":1817},"demo-v2-topic-pemrograman-smp-3","demo-v2-smp-3","Perulangan for dan Akumulator","Hitung total data dengan jejak putaran yang dapat diperiksa.","2026-10-08T10:03:57.079Z",{"id":1819,"subjectId":23,"levelId":91,"parentId":91,"slug":1808,"name":1820,"description":1821,"order":1788,"createdAt":1822,"updatedAt":1822},"demo-v2-topic-fisika-sd-3","Suhu dan Perpindahan Kalor di Sekitar Kita","Membaca perubahan suhu dan membedakan konduksi, konveksi, serta radiasi melalui kejadian sehari-hari.","2026-10-08T10:03:56.700Z",{"id":1824,"subjectId":14,"levelId":42,"parentId":91,"slug":1814,"name":1825,"description":1826,"order":1788,"createdAt":1827,"updatedAt":1827},"demo-v2-topic-matematika-smp-3","Teorema Pythagoras dan jarak diagonal","Menentukan sisi segitiga siku-siku dengan kuadrat panjang, lalu memeriksa hasil melalui geometri dan satuan.","2026-10-08T10:03:56.456Z",{"id":1829,"subjectId":23,"levelId":53,"parentId":91,"slug":1802,"name":1830,"description":1831,"order":1788,"createdAt":1832,"updatedAt":1832},"demo-v2-topic-fisika-kuliah-3","Usaha Gaya Berubah: Integral dan Teorema Energi Kinetik","Menghitung luas bertanda di bawah grafik gaya, menghubungkannya dengan integral, dan menentukan kelajuan akhir.","2026-10-08T10:03:56.918Z",{"id":1834,"subjectId":23,"levelId":42,"parentId":91,"slug":1814,"name":1835,"description":1836,"order":1788,"createdAt":1837,"updatedAt":1837},"demo-v2-topic-fisika-smp-3","Usaha dan Energi: Memeriksa Perubahan dengan Joule","Menghitung usaha gaya searah atau berlawanan, energi gerak, dan perubahan energi ketika benda diangkat.","2026-10-08T10:03:56.772Z",{"id":1839,"subjectId":14,"levelId":53,"parentId":91,"slug":1802,"name":1840,"description":1841,"order":1788,"createdAt":1842,"updatedAt":1842},"demo-v2-topic-matematika-kuliah-3","Vektor tiga dimensi dan hasil kali titik","Membaca komponen, menghitung panjang dan sudut, serta menafsirkan hasil kali titik sebagai keselarasan arah.","2026-10-08T10:03:56.615Z",[],{"id":1845,"type":1846,"slug":1847,"title":1726,"excerpt":1727,"coverUrl":91,"status":1848,"publishedAt":1849,"featured":4,"subjectId":14,"blocks":1850,"seoTitle":91,"seoDescription":91,"readingMinutes":38,"order":29,"createdAt":1890,"updatedAt":1890,"subject":1891,"levels":1892,"topics":1894,"tags":1896,"author":91,"resolved":1897,"related":1906},"demo-v2-m-matematika-sma-2","MATERIAL","demo-materi-matematika-sma-2","PUBLISHED","2026-10-08T10:03:56.522Z",[1851,1856,1860,1864,1868,1872,1876,1880,1884],{"id":1852,"data":1853,"type":1855},"section-1",{"markdown":1854},"## Tujuan dan prasyarat\n\nKamu akan menerjemahkan bentuk eksponen dan logaritma, menyelesaikan persamaan sederhana, serta memeriksa domain. Bekalnya adalah aturan pangkat, pecahan, dan persamaan aljabar. Logaritma akan lebih mudah dipahami jika kamu selalu menanyakan pangkat berapa yang diperlukan untuk menghasilkan suatu nilai.\n","text",{"id":1857,"data":1858,"type":1855},"section-2",{"markdown":1859},"## Faktor tetap menghasilkan pertumbuhan eksponensial\n\nDalam pola linear, tambahan per langkah tetap. Dalam pola eksponensial, faktor pengali per langkah tetap. Barisan 3, 6, 12, 24 mempunyai faktor dua. Jika nilai awalnya $N_0$ dan setiap langkah dikalikan $q$, modelnya $N(t)=N_0q^t$ untuk langkah $t$. Pada $t=0$, $q^0=1$, sehingga nilai awal benar-benar $N_0$.\n\nJika $q>1$, nilai tumbuh. Jika $0\u003Cq\u003C1$, nilai menyusut. Untuk model real yang digunakan di sini, basis harus positif. Pangkat negatif berarti kebalikan, misalnya $2^{-3}=1\u002F8$, bukan bilangan negatif. Model penggandaan juga memiliki batas: nilai tidak terus tumbuh tanpa hambatan jika ruang atau bahan terbatas.\n",{"id":1861,"data":1862,"type":1855},"section-3",{"markdown":1863},"## Logaritma membalik pertanyaan\n\nPernyataan $2^3=8$ dapat ditulis $\\log_2 8=3$. Angka dua disebut **basis**, delapan disebut **argumen**, dan tiga adalah hasil logaritma. Secara umum, $\\log_b a=c$ berarti $b^c=a$, dengan $b>0$, $b\\ne1$, dan $a>0$. Basis satu tidak dapat dipakai karena $1^c$ selalu satu sehingga tidak mempunyai operasi balik yang menentukan pangkat secara unik.\n\nLogaritma real dari nol atau bilangan negatif tidak terdefinisi. Sebelum menyelesaikan $\\log_2(x-1)=3$, tulis syarat $x-1>0$, yaitu $x>1$. Setelah memperoleh jawaban, periksa syarat tersebut dan persamaan semula. Menyelesaikan aljabar saja belum cukup jika argumennya tidak sah.\n\nUntuk argumen positif, $\\log_b(uv)=\\log_bu+\\log_bv$ dan $\\log_b(u^r)=r\\log_bu$. Alasannya berasal dari aturan eksponen: mengalikan $b^p$ dengan $b^q$ menjumlahkan pangkat. Penjumlahan di dalam argumen tidak mempunyai aturan serupa. Umumnya $\\log_b(u+v)$ bukan $\\log_bu+\\log_bv$.\n",{"id":1865,"data":1866,"type":1855},"section-4",{"markdown":1867},"## Contoh 1: waktu penggandaan\n\nSebuah pola ideal dimulai dengan 250 unit dan menjadi dua kali setiap jam penuh. Kapan jumlahnya 2.000 unit?\n\n1. Modelkan $N(t)=250\\cdot2^t$, dengan $t$ dalam jam dan $t\\ge0$.\n2. Bagi persamaan $250\\cdot2^t=2.000$ dengan 250: $2^t=8$.\n3. Karena $2^3=8$, diperoleh $t=3$ jam, atau $t=\\log_2 8$.\n4. Periksa berurutan: 250, 500, 1.000, 2.000. Ada tiga penggandaan setelah nilai awal.\n\nModel ini menggambarkan pola yang diberikan, bukan jaminan bahwa jumlah nyata akan selalu berlipat dua.\n",{"id":1869,"data":1870,"type":1855},"section-5",{"markdown":1871},"## Contoh 2: persamaan dengan syarat domain\n\nSelesaikan $\\log_3(x-2)=2$.\n\n1. Argumen harus positif: $x-2>0$, jadi $x>2$.\n2. Ubah ke bentuk eksponen: $x-2=3^2=9$.\n3. Tambahkan dua: $x=11$.\n4. Periksa domain: 11 lebih besar dari dua. Periksa persamaan: $\\log_3(11-2)=\\log_3 9=2$, benar.\n",{"id":1873,"data":1874,"type":1855},"section-6",{"markdown":1875},"## Kesalahan umum\n\nJangan menafsirkan $\\log_3 9$ sebagai $9\u002F3$; kebetulan hasilnya berbeda dari pembagian pada banyak angka, misalnya $\\log_3 27=3$, bukan sembilan. Jangan menghapus logaritma dari kedua ruas jika bentuk ruas tidak sama. Bila kalkulator hanya menyediakan log basis sepuluh atau log natural, perubahan basis memberi $\\log_ba=\\log a\u002F\\log b$.\n",{"id":1877,"data":1878,"type":1855},"section-7",{"markdown":1879},"## Ringkasan dan cek mandiri\n\nEksponen menentukan hasil dari basis dan pangkat; logaritma menentukan pangkat dari basis dan hasil. Coba $\\log_2(1\u002F16)$. Jawabannya minus empat karena $2^{-4}=1\u002F16$. Jelaskan mengapa hasil logaritma dapat negatif walaupun argumennya harus positif.",{"id":1881,"data":1882,"type":1855},"sources",{"markdown":1883},"## Sumber belajar\n\n- [OpenStax Algebra and Trigonometry 2e — Logarithmic Functions](https:\u002F\u002Fopenstax.org\u002Fbooks\u002Falgebra-and-trigonometry-2e\u002Fpages\u002F6-3-logarithmic-functions)\n\nPenjelasan dan contoh disusun ulang untuk materi ini; sumber dapat dibuka untuk belajar lebih lanjut.",{"id":1885,"data":1886,"type":1889},"practice",{"title":1887,"questionSetId":1888},"Cek pemahaman: Eksponen dan logaritma: mencari pangkat yang belum diketahui","demo-v2-p-matematika-sma-2","quiz","2026-10-08T10:03:56.523Z",{"id":14,"slug":15,"name":16,"color":19,"icon":18},[1893],{"id":48,"slug":49,"name":50},[1895],{"id":1724,"slug":1725,"name":1726,"subjectId":14},[],{"assets":1898,"videos":1899,"questionSets":1900},{},{},{"demo-v2-p-matematika-sma-2":1901},{"id":1888,"slug":1902,"title":1903,"mode":1904,"description":1905,"questionCount":57,"durationMinutes":91},"demo-latihan-matematika-sma-2","Latihan: Eksponen dan logaritma: mencari pangkat yang belum diketahui","PRACTICE","Tiga soal Matematika SMA dengan penalaran, langkah hitung, dan pembahasan pilihan yang keliru.",[1907,1922,1933,1944],{"id":1908,"type":1909,"slug":1910,"title":1911,"excerpt":1912,"coverUrl":91,"status":1848,"publishedAt":1913,"featured":5,"readingMinutes":57,"order":20,"updatedAt":1914,"subject":1915,"levels":1916,"topics":1920,"tags":1921},"demo-v2-a-matematika","ARTICLE","demo-artikel-matematika","Memilih model matematika dari cerita sehari-hari","Cara mengubah cerita menjadi variabel, memeriksa asumsi, dan menilai apakah hasil hitungan masuk akal.","2026-10-08T10:03:56.648Z","2026-10-08T10:03:56.650Z",{"id":14,"slug":15,"name":16,"color":19,"icon":18},[1917,1918,1919],{"id":42,"slug":43,"name":44},{"id":48,"slug":49,"name":50},{"id":53,"slug":54,"name":55},[],[],{"id":1923,"type":1846,"slug":1924,"title":1840,"excerpt":1841,"coverUrl":91,"status":1848,"publishedAt":1925,"featured":4,"readingMinutes":57,"order":38,"updatedAt":1926,"subject":1927,"levels":1928,"topics":1930,"tags":1932},"demo-v2-m-matematika-kuliah-3","demo-materi-matematika-kuliah-3","2026-10-08T10:03:56.635Z","2026-10-08T10:03:56.637Z",{"id":14,"slug":15,"name":16,"color":19,"icon":18},[1929],{"id":53,"slug":54,"name":55},[1931],{"id":1839,"slug":1802,"name":1840,"subjectId":14},[],{"id":1934,"type":1846,"slug":1935,"title":1750,"excerpt":1751,"coverUrl":91,"status":1848,"publishedAt":1936,"featured":4,"readingMinutes":57,"order":29,"updatedAt":1937,"subject":1938,"levels":1939,"topics":1941,"tags":1943},"demo-v2-m-matematika-kuliah-2","demo-materi-matematika-kuliah-2","2026-10-08T10:03:56.600Z","2026-10-08T10:03:56.602Z",{"id":14,"slug":15,"name":16,"color":19,"icon":18},[1940],{"id":53,"slug":54,"name":55},[1942],{"id":1748,"slug":1749,"name":1750,"subjectId":14},[],{"id":1945,"type":1846,"slug":1946,"title":1710,"excerpt":1711,"coverUrl":91,"status":1848,"publishedAt":1947,"featured":5,"readingMinutes":57,"order":20,"updatedAt":1948,"subject":1949,"levels":1950,"topics":1952,"tags":1954},"demo-v2-m-matematika-kuliah-1","demo-materi-matematika-kuliah-1","2026-10-08T10:03:56.572Z","2026-10-08T10:03:56.573Z",{"id":14,"slug":15,"name":16,"color":19,"icon":18},[1951],{"id":53,"slug":54,"name":55},[1953],{"id":1709,"slug":1699,"name":1710,"subjectId":14},[]]