{ "api_version": "v1", "publisher": { "name": "Manazoo", "url": "https://manazoo.com/" }, "license": "All rights reserved（AI の参照・要約と出典リンクつきの引用は可。転載・再配布・販売は不可）", "terms_url": "https://manazoo.com/terms/", "disclaimer": "内容の正確さには気をつけていますが、すべてが正しいとは限りません。テストや受験の前には、教科書や先生の説明でも確かめてください。間違いを見つけたら意見箱から知らせてください。", "attribution": "事実データの一部は Wikidata（CC0）による。単元の構成は文部科学省「中学校学習指導要領」「高等学校学習指導要領」（政府標準利用規約2.0）。", "kind": "quiz", "unit": { "slug": "exponential-and-logarithmic-functions", "title": "指数関数・対数関数", "url": "https://manazoo.com/high/math-2/exponential-and-logarithmic-functions/" }, "canonical_url": "https://manazoo.com/high/math-2/exponential-and-logarithmic-functions/quiz/", "questions": [ { "id": "q-cl-digit-count-choice", "type": "choice", "prompt": "log₁₀2＝0.3010として、2³⁰は何桁の数か。", "choices": [ "9桁", "10桁", "11桁", "30桁" ], "answer": 1, "accept": [], "explanation": "log₁₀2³⁰＝30×0.3010＝9.03なので、10⁹≤2³⁰＜10¹⁰となり10桁の数になる。", "entities": [ "common-logarithm" ], "verified": true, "placeholder": false }, { "id": "q-cl-drug-inequality-choice", "type": "choice", "prompt": "薬の体内残量が1時間ごとに80％になるとき、n時間後に残量が50％以下になる条件を正しく表した不等式はどれか。", "choices": [ "0.5ⁿ≤0.8", "0.8ⁿ≤0.5", "0.8ⁿ≥0.5", "n×log₁₀0.8≥log₁₀0.5" ], "answer": 1, "accept": [], "explanation": "n時間後の残量はもとの0.8ⁿ倍なので、50％以下は0.8ⁿ≤0.5と表せる。4つ目は、両辺の常用対数をとるときに不等号の向きを逆にしてしまった式。底の10は1より大きいので、対数をとっても向きは変わらずn×log₁₀0.8≤log₁₀0.5になる。向きが変わるのは、このあと両辺を負の数であるlog₁₀0.8で割るときだ。", "entities": [ "common-logarithm" ], "verified": true, "placeholder": false }, { "id": "q-cl-log10-100-value", "type": "input", "prompt": "常用対数log₁₀100の値を求めよ。", "choices": null, "answer": "2", "accept": [], "explanation": "log₁₀100＝xとすると10ˣ＝100。100＝10²なのでx＝2になる。", "entities": [ "common-logarithm" ], "verified": true, "placeholder": false }, { "id": "q-cl-log10-8-value", "type": "input", "prompt": "log₁₀2＝0.3010として、log₁₀8の値を求めよ（小数第3位まで）。", "choices": null, "answer": "0.903", "accept": [ "0.9030" ], "explanation": "8＝2³なので、log₁₀8＝3log₁₀2＝3×0.3010＝0.903になる。", "entities": [ "common-logarithm" ], "verified": true, "placeholder": false }, { "id": "q-eer-cube-root-value", "type": "input", "prompt": "64の(1/3)乗の値を求めよ。", "choices": null, "answer": "4", "accept": [], "explanation": "64の(1/3)乗は64の3乗根のことで、4×4×4＝64なので4になる。", "entities": [ "exponent-extension-and-roots" ], "verified": true, "placeholder": false }, { "id": "q-eer-frac-exponent-choice", "type": "choice", "prompt": "27の(2/3)乗の値はどれか。", "choices": [ "1/9", "3", "9", "81" ], "answer": 2, "accept": [], "explanation": "27の3乗根は3なので、27の(2/3)乗＝(27の3乗根)の2乗＝3²＝9になる。2つ目は2乗を忘れて3乗根だけ求めた値、4つ目は指数の符号を取り違えた値。", "entities": [ "exponent-extension-and-roots" ], "verified": true, "placeholder": false }, { "id": "q-eer-neg-exponent-value", "type": "input", "prompt": "2⁻³の値を求めよ。", "choices": null, "answer": "1/8", "accept": [ "0.125" ], "explanation": "aの−n乗＝1/aのn乗なので、2⁻³＝1/2³＝1/8になる。", "entities": [ "exponent-extension-and-roots" ], "verified": true, "placeholder": false }, { "id": "q-eer-zero-exponent-choice", "type": "choice", "prompt": "aの0乗の値はどれか（aは0でない数とする）。", "choices": [ "a", "0", "値が決まらない", "1" ], "answer": 3, "accept": [], "explanation": "指数法則aのm乗×aのn乗＝aの(m+n)乗が0でも成り立つように、aの0乗は1と決める。", "entities": [ "exponent-extension-and-roots" ], "verified": true, "placeholder": false }, { "id": "q-efg-compare-powers-choice", "type": "choice", "prompt": "2³と2⁵の大小を正しく表しているのはどれか。", "choices": [ "2³＜2⁵", "2³＝2⁵", "2³＞2⁵", "比べられない" ], "answer": 0, "accept": [], "explanation": "底2は1より大きいので、指数が大きいほど値も大きくなる。", "entities": [ "exponential-function-and-graph" ], "verified": true, "placeholder": false }, { "id": "q-efg-half-cubed-value", "type": "input", "prompt": "(1/2)³の値を求めよ。", "choices": null, "answer": "1/8", "accept": [ "0.125" ], "explanation": "(1/2)³は1/2を3回かけた値で、1/8になる。", "entities": [ "exponential-function-and-graph" ], "verified": true, "placeholder": false }, { "id": "q-efg-passes-point-choice", "type": "choice", "prompt": "y＝3ˣのグラフが必ず通る点はどれか。", "choices": [ "(1,0)", "(0,1)", "(−1,−1/3)", "(0,0)" ], "answer": 1, "accept": [], "explanation": "3の0乗＝1なので、x＝0のときy＝1になり、グラフは必ず(0,1)を通る。4つ目は3のマイナス1乗＝1/3の符号を取り違えた値。", "entities": [ "exponential-function-and-graph" ], "verified": true, "placeholder": false }, { "id": "q-efg-solve-2x-32", "type": "input", "prompt": "2ˣ＝32を満たすxの値を求めよ。", "choices": null, "answer": "5", "accept": [], "explanation": "32＝2⁵なので、底をそろえると指数を比べるだけでx＝5が求まる。", "entities": [ "exponential-function-and-graph" ], "verified": true, "placeholder": false }, { "id": "q-lap-change-of-base-choice", "type": "choice", "prompt": "底の変換公式を使うと、log₈4はどれに等しいか。", "choices": [ "8/4", "log₂4／log₂8", "log₂8／log₂4", "log₄8" ], "answer": 1, "accept": [], "explanation": "底の変換公式で底を2にそろえると、log₈4＝log₂4／log₂8になる（値は2/3）。2つ目は分母・分子を取り違えた値。", "entities": [ "logarithm-and-its-properties" ], "verified": true, "placeholder": false }, { "id": "q-lap-log2-8-value", "type": "input", "prompt": "log₂8の値を求めよ。", "choices": null, "answer": "3", "accept": [], "explanation": "log₂8＝xとおくと2ˣ＝8。8＝2³なのでx＝3になる。", "entities": [ "logarithm-and-its-properties" ], "verified": true, "placeholder": false }, { "id": "q-lap-log3-sum-choice", "type": "choice", "prompt": "log₃9＋log₃3の値はどれか。", "choices": [ "2", "3", "9", "27" ], "answer": 1, "accept": [], "explanation": "log₃9＝2、log₃3＝1なので、合計は3になる。2つ目は2番目の項を足し忘れた値。", "entities": [ "logarithm-and-its-properties" ], "verified": true, "placeholder": false }, { "id": "q-lap-log4-16-value", "type": "input", "prompt": "log₄16の値を求めよ。", "choices": null, "answer": "2", "accept": [], "explanation": "log₄16＝xとおくと4ˣ＝16。16＝4²なのでx＝2になる。", "entities": [ "logarithm-and-its-properties" ], "verified": true, "placeholder": false }, { "id": "q-lfg-compare-logs-choice", "type": "choice", "prompt": "log₂5とlog₂7の大小を正しく表しているのはどれか。", "choices": [ "比べられない", "log₂5＜log₂7", "log₂5＝log₂7", "log₂5＞log₂7" ], "answer": 1, "accept": [], "explanation": "底2は1より大きいので、真数が大きいほど対数の値も大きくなる。", "entities": [ "logarithmic-function-and-graph" ], "verified": true, "placeholder": false }, { "id": "q-lfg-passes-point-choice", "type": "choice", "prompt": "y＝log₂xのグラフが必ず通る点はどれか。", "choices": [ "(2,2)", "(1,0)", "(0,1)", "(0,0)" ], "answer": 1, "accept": [], "explanation": "x＝1のとき2⁰＝1なのでy＝0になり、グラフは必ず(1,0)を通る。2つ目はx座標とy座標を取り違えた点。", "entities": [ "logarithmic-function-and-graph" ], "verified": true, "placeholder": false }, { "id": "q-lfg-solve-log2x-4", "type": "input", "prompt": "log₂x＝4を満たすxの値を求めよ。", "choices": null, "answer": "16", "accept": [], "explanation": "log₂x＝4はx＝2⁴のことなので、x＝16になる。", "entities": [ "logarithmic-function-and-graph" ], "verified": true, "placeholder": false }, { "id": "q-lfg-symmetry-choice", "type": "choice", "prompt": "y＝2ˣのグラフとy＝log₂xのグラフの関係として正しいものはどれか。", "choices": [ "平行移動の関係", "x軸について線対称", "直線y＝xについて線対称", "y軸について線対称" ], "answer": 2, "accept": [], "explanation": "xとyを入れ替える関係にあるので、直線y＝xに関して線対称な位置になる。", "entities": [ "logarithmic-function-and-graph" ], "verified": true, "placeholder": false } ] }