{"id":1155,"date":"2026-01-18T20:02:09","date_gmt":"2026-01-18T10:02:09","guid":{"rendered":"https:\/\/archive4ones.com\/2ndstudy\/?p=1155"},"modified":"2026-01-21T21:49:28","modified_gmt":"2026-01-21T11:49:28","slug":"year11-math-3-1-4-chapter4-exponential-and-logarithmic-functions-jp","status":"publish","type":"post","link":"https:\/\/archive4ones.com\/2ndstudy\/?p=1155","title":{"rendered":"Year11-MATH-3-1-4 Chapter4 Exponential and Logarithmic Functions-JP"},"content":{"rendered":"\n

\u7b2c4\u7ae0\uff1a\u6307\u6570\u95a2\u6570\u3068\u5bfe\u6570\u95a2\u6570<\/h3>\n\n\n\n

\u3053\u308c\u307e\u3067\u306e\u7ae0\u3067\u306f\u3001x<\/mi>2<\/mn><\/msup>x^2<\/annotation><\/semantics><\/math> \u3084 x<\/mi>3<\/mn><\/msup>x^3<\/annotation><\/semantics><\/math>\u306e\u3088\u3046\u306a\u591a\u9805\u5f0f\u95a2\u6570\u306b\u7126\u70b9\u3092\u5f53\u3066\u3066\u304d\u307e\u3057\u305f\u3002\u7b2c4\u7ae0\u3067\u306f\u3001\u5909\u6570\u304c \u6307\u6570<\/strong> \u3067\u3042\u308b\u95a2\u6570\u306b\u3064\u3044\u3066\u8003\u5bdf\u3057\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u95a2\u6570\u306f\u3001\u4eba\u53e3\u5897\u52a0\u3001\u653e\u5c04\u6027\u5d29\u58ca\u3001\u8907\u5229\u306e\u30e2\u30c7\u30eb\u5316\u306b\u4e0d\u53ef\u6b20\u3067\u3059\u3002<\/p>\n\n\n\n
\n\n\n\n

4.1 \u6307\u6570\u95a2\u6570\u3068\u6570e<\/mi>e<\/annotation><\/semantics><\/math><\/h4>\n\n\n\n

\u6307\u6570\u95a2\u6570\u306f f<\/mi>(<\/mo>x<\/mi>)<\/mo>=<\/mo>a<\/mi>x<\/mi><\/msup><\/mrow>f(x)=a^x<\/annotation><\/semantics><\/math>\u306e\u5f62\u3092\u3068\u308a\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u6570\u5b66\u7684\u624b\u6cd5\u3067\u306f\u3001\u4e3b\u306b \u81ea\u7136\u6307\u6570\u5e95<\/strong> \u3067\u3042\u308b e<\/mi>e<\/annotation><\/semantics><\/math>\u306b\u7126\u70b9\u3092\u5f53\u3066\u307e\u3059\u3002<\/p>\n\n\n\n
    \n
  • \u5b9a\u6570<\/strong>e<\/mi>e<\/annotation><\/semantics><\/math> :<\/strong> \u306f\u304a\u3088\u305d 2.71828<\/mn><\/semantics><\/math>\u3067\u3059\u3002\u95a2\u6570\u306e\u52fe\u914d\u306f\u3001\u3069\u306e\u70b9\u306b\u304a\u3044\u3066\u3082\u95a2\u6570\u306e\u5024\u3068\u5b8c\u5168\u306b\u4e00\u81f4\u3059\u308b\u305f\u3081\u3001f<\/mi>(<\/mo>x<\/mi>)<\/mo>=<\/mo>e<\/mi>x<\/mi><\/mrow>f(x)=ex<\/annotation><\/semantics><\/math> \u306f\u552f\u4e00\u306e\u6570\u3067\u3059\u3002<\/li>\n\n\n\n
  • \u6f38\u8fd1\u7dda:<\/strong> y<\/mi>=<\/mo>e<\/mi>x<\/mi><\/mrow>y=ex<\/annotation><\/semantics><\/math> \u306e\u30b0\u30e9\u30d5\u306f – \u8ef8\u306b\u63a5\u3059\u308b\u3053\u3068\u306f\u306a\u304f\u3001y<\/mi>=<\/mo>0<\/mn><\/mrow>y=0<\/annotation><\/semantics><\/math> \u3067\u6c34\u5e73\u6f38\u8fd1\u7dda\u3092\u6301\u3061\u307e\u3059\u3002<\/li>\n<\/ul>\n\n\n\n
    \n\n\n\n

    4.2 \u5bfe\u6570\u95a2\u6570<\/h4>\n\n\n\n

    \u5bfe\u6570\u306f\u6307\u6570\u95a2\u6570\u306e \u9006\u6570<\/strong> \u3067\u3059\u3002y<\/mi>=<\/mo>e<\/mi>x<\/mi><\/mrow>y=ex<\/annotation><\/semantics><\/math> \u306a\u3089\u3070 x<\/mi>=<\/mo>l<\/mi>n<\/mi>\u2061<\/mtext>(<\/mo>y<\/mi>)<\/mo><\/mrow>x=ln\u2061(y)<\/annotation><\/semantics><\/math>\u3067\u3059\u3002<\/p>\n\n\n\n
      \n
    • l<\/mi>n<\/mi>\u2061<\/mtext>(<\/mo>x<\/mi>)<\/mo><\/mrow>ln\u2061(x)<\/annotation><\/semantics><\/math>** (\u81ea\u7136\u5bfe\u6570):** \u3053\u308c\u306f e<\/mi>e<\/annotation><\/semantics><\/math>\u3092\u5e95\u3068\u3059\u308b\u5bfe\u6570\u3067\u3059\u3002<\/li>\n\n\n\n
    • \u5b9a\u7fa9\u57df\u3068\u5024\u57df:<\/strong> \u8ca0\u306e\u6570\u307e\u305f\u306f\u30bc\u30ed\u306e\u5bfe\u6570\u306f\u3068\u308c\u307e\u305b\u3093\u3002\u3057\u305f\u304c\u3063\u3066\u3001f<\/mi>(<\/mo>x<\/mi>)<\/mo>=<\/mo>l<\/mi>n<\/mi>\u2061<\/mtext>(<\/mo>x<\/mi>)<\/mo><\/mrow>f(x)=ln\u2061(x)<\/annotation><\/semantics><\/math> \u306e\u5834\u5408\u3001\u5b9a\u7fa9\u57df\u306f x<\/mi>><\/mo>0<\/mn><\/mrow>x>0<\/annotation><\/semantics><\/math>\u3067\u3059\u3002<\/li>\n<\/ul>\n\n\n\n
      \n\n\n\n

      4.3 \u5bfe\u6570\u6cd5\u5247<\/h4>\n\n\n\n

      e<\/mi>e<\/annotation><\/semantics><\/math>\u304a\u3088\u3073 l<\/mi>n<\/mi><\/mrow>ln<\/annotation><\/semantics><\/math>\u3092\u542b\u3080\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u306b\u306f\u3001\u5bfe\u6570\u6cd5\u5247\u3092\u7fd2\u5f97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u6cd5\u5247\u306f\u5e95\u306b\u95a2\u308f\u3089\u305a\u540c\u3058\u3067\u3059\u304c\u3001\u81ea\u7136\u5bfe\u6570\u3067\u6700\u3082\u3088\u304f\u7528\u3044\u3089\u308c\u307e\u3059\u3002<\/p>\n\n\n\n
        \n
      1. \u7a4d\u306e\u6cd5\u5247:<\/strong> l<\/mi>n<\/mi>\u2061<\/mtext>(<\/mo>a<\/mi>b<\/mi>)<\/mo>=<\/mo>l<\/mi>n<\/mi>\u2061<\/mtext>(<\/mo>a<\/mi>)<\/mo>+<\/mo>l<\/mi>n<\/mi>\u2061<\/mtext>(<\/mo>b<\/mi>)<\/mo><\/mrow>ln\u2061(ab)=ln\u2061(a)+ln\u2061(b)<\/annotation><\/semantics><\/math><\/li>\n\n\n\n
      2. \u5546\u306e\u6cd5\u5247:<\/strong> l<\/mi>n<\/mi>\u2061<\/mtext>(<\/mo>a<\/mi>b<\/mi><\/mfrac>)<\/mo>=<\/mo>l<\/mi>n<\/mi>\u2061<\/mtext>(<\/mo>a<\/mi>)<\/mo>\u2212<\/mo>l<\/mi>n<\/mi>\u2061<\/mtext>(<\/mo>b<\/mi>)<\/mo><\/mrow>ln\u2061(\\frac{a}{b})=ln\u2061(a)\u2212ln\u2061(b)<\/annotation><\/semantics><\/math><\/li>\n\n\n\n
      3. \u3079\u304d\u4e57\u306e\u6cd5\u5247:<\/strong> l<\/mi>n<\/mi>\u2061<\/mtext>(<\/mo>a<\/mi>n<\/mi><\/msup>)<\/mo>=<\/mo>n<\/mi>l<\/mi>n<\/mi>\u2061<\/mtext>(<\/mo>a<\/mi>)<\/mo><\/mrow>ln\u2061(a^n)=nln\u2061(a)<\/annotation><\/semantics><\/math><\/li>\n\n\n\n
      4. \u9006\u306e\u6027\u8cea:<\/strong> \u304a\u3088\u3073 l<\/mi>n<\/mi>\u2061<\/mtext>(<\/mo>e<\/mi>x<\/mi><\/msup>)<\/mo>=<\/mo>x<\/mi>a<\/mi>n<\/mi>d<\/mi> <\/mtext>e<\/mi>l<\/mi>n<\/mi>\u2061<\/mtext>(<\/mo>x<\/mi>)<\/mo><\/mrow><\/msup>=<\/mo>x<\/mi><\/mrow>ln\u2061(e^x)=x and\\ e^{ln\u2061(x)}=x<\/annotation><\/semantics><\/math><\/li>\n<\/ol>\n\n\n\n
        \n

        \u4f8b\u984c 1: <\/strong>x<\/mi>x<\/annotation><\/semantics><\/math>\u3092\u89e3\u304f<\/strong>
        5<\/mn>e<\/mi>2<\/mn>x<\/mi><\/mrow><\/msup>=<\/mo>20<\/mn><\/mrow>5e^{2x}=20<\/annotation><\/semantics><\/math>\u3092\u89e3\u304d\u307e\u3059\u3002<\/p>\n\n\n\n
          \n
        1. 5<\/mn>e<\/mi>2<\/mn>x<\/mi><\/mrow><\/msup><\/mrow>5e^{2x}<\/annotation><\/semantics><\/math>\u3092 5 \u3067\u5272\u308a\u307e\u3059\u3002e<\/mi>2<\/mn>x<\/mi><\/mrow><\/msup>e^{2x}<\/annotation><\/semantics><\/math>=<\/mo>4<\/mn><\/mrow>=4<\/annotation><\/semantics><\/math><\/li>\n\n\n\n
        2. \u4e21\u8fba\u306e\u81ea\u7136\u5bfe\u6570\u3092\u3068\u308a\u307e\u3059\u3002l<\/mi>n<\/mi>\u2061<\/mtext>(<\/mo>e<\/mi>2<\/mn>x<\/mi><\/mrow><\/msup>)<\/mo>=<\/mo>l<\/mi>n<\/mi>\u2061<\/mtext>(<\/mo>4<\/mn>)<\/mo><\/mrow>ln\u2061(e^{2x})=ln\u2061(4)<\/annotation><\/semantics><\/math><\/li>\n\n\n\n
        3. \u9006\u306e\u6027\u8cea\u3092\u4f7f\u7528\u3057\u307e\u3059\u30022<\/mn>x<\/mi>=<\/mo>l<\/mi>n<\/mi>(<\/mo>4<\/mn>)<\/mo><\/mrow>2x = ln(4)<\/annotation><\/semantics><\/math><\/li>\n\n\n\n
        4. x<\/mi>x<\/annotation><\/semantics><\/math>\u3092\u89e3\u304d\u307e\u3059\u3002x<\/mi>=<\/mo>l<\/mi>n<\/mi>\u2061<\/mtext>(<\/mo>4<\/mn>)<\/mo><\/mrow>2<\/mn><\/mfrac>\u2248<\/mo>0.693<\/mn><\/mrow>x=\\frac{ln\u2061(4)}{2}\u22480.693<\/annotation><\/semantics><\/math><\/li>\n<\/ol>\n<\/blockquote>\n\n\n\n
          \n\n\n\n

          4.4 e<\/mi>x<\/mi><\/msup>e^x<\/annotation><\/semantics><\/math>\u3068l<\/mi>n<\/mi>(<\/mo>x<\/mi>)<\/mo><\/mrow>ln(x)<\/annotation><\/semantics><\/math> \u306e\u5fae\u5206<\/h4>\n\n\n\n

          \u5fae\u7a4d\u5206\u306f e<\/mi>e<\/annotation><\/semantics><\/math>\u3092\u5e95\u3068\u3059\u308b\u5834\u5408\u306b\u975e\u5e38\u306b\u7c21\u6f54\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n
            \n
          • ** e<\/mi>x<\/mi><\/msup>e^x<\/annotation><\/semantics><\/math> \u306e\u5fae\u5206 :<\/mo>d<\/mi>d<\/mi>x<\/mi><\/mrow><\/mfrac>(<\/mo>e<\/mi>k<\/mi>x<\/mi><\/mrow><\/msup>)<\/mo>=<\/mo>k<\/mi>e<\/mi>k<\/mi>x<\/mi><\/mrow><\/msup><\/mrow>: \\frac{d}{dx}(e^{kx})=ke^{kx}<\/annotation><\/semantics><\/math>** (\u57fa\u672c\u7684\u306b\u95a2\u6570\u306f\u540c\u3058\u3067\u3059\u304c\u3001\u6307\u6570\u306e\u5fae\u5206\u3092\u639b\u3051\u307e\u3059\u3002)<\/em><\/li>\n\n\n\n
          • ** l<\/mi>n<\/mi>(<\/mo>x<\/mi>)<\/mo><\/mrow>ln(x)<\/annotation><\/semantics><\/math> \u306e\u5fae\u5206 :<\/mo>d<\/mi>d<\/mi>x<\/mi><\/mrow><\/mfrac>(<\/mo>l<\/mi>n<\/mi>(<\/mo>x<\/mi>)<\/mo>)<\/mo>=<\/mo>1<\/mn>x<\/mi><\/mfrac><\/mrow>: \\frac{d}{dx}(ln(x))=\\frac{1}{x}<\/annotation><\/semantics><\/math> :**<\/li>\n<\/ul>\n\n\n\n
            \n

            \u6f14\u7fd2\u4f8b 2: \u5fae\u5206<\/strong>
            f<\/mi>(<\/mo>x<\/mi>)<\/mo>=<\/mo>e<\/mi>5<\/mn>x<\/mi><\/mrow><\/msup>+<\/mo>l<\/mi>n<\/mi>(<\/mo>x<\/mi>)<\/mo><\/mrow>f(x) = e^{5x} + ln(x)<\/annotation><\/semantics><\/math>\u3092\u5fae\u5206\u3057\u307e\u3059\u3002<\/p>\n\n\n\n
              \n
            1. e<\/mi>5<\/mn>x<\/mi><\/mrow><\/msup>e^{5x}<\/annotation><\/semantics><\/math>\u3092\u5fae\u5206\u3057\u307e\u3059\u3002\u3079\u304d\u4e57 (5<\/mn>x<\/mi><\/mrow>5x<\/annotation><\/semantics><\/math>) \u306e\u5fae\u5206\u306f 5 \u3067\u3059\u3002\u7d50\u679c: 5<\/mn>e<\/mi>5<\/mn>x<\/mi><\/mrow><\/msup><\/mrow>5e^{5x}<\/annotation><\/semantics><\/math>\u3002<\/li>\n\n\n\n
            2. ln(x) \u3092\u5fae\u5206\u3057\u307e\u3059\u3002\u7d50\u679c:\u30001<\/mn>x<\/mi><\/mfrac> \\frac{1}{x} <\/annotation><\/semantics><\/math>\u3002<\/li>\n\n\n\n
            3. \u6700\u7d42\u89e3\u7b54:<\/strong> f<\/mi>\u2032<\/mtext>(<\/mo>x<\/mi>)<\/mo>=<\/mo>5<\/mn>e<\/mi>5<\/mn>x<\/mi><\/mrow><\/msup>+<\/mo>1<\/mn>x<\/mi><\/mfrac><\/mrow>f\u2032(x)=5e^{5x} +\\frac{1}{x}<\/annotation><\/semantics><\/math>\u3002<\/li>\n<\/ol>\n<\/blockquote>\n\n\n\n
              \n\n\n\n

              4.5 \u7df4\u7fd2\u554f\u984c<\/h4>\n\n\n\n

              \u30d1\u30fc\u30c8 A: \u4ee3\u6570\u3068\u5bfe\u6570\u6cd5\u5247<\/h5>\n\n\n\n
                \n
              1. 2<\/mn>l<\/mi>n<\/mi>\u2061<\/mtext>(<\/mo>x<\/mi>)<\/mo>+<\/mo>l<\/mi>n<\/mi>\u2061<\/mtext>(<\/mo>y<\/mi>)<\/mo><\/mrow>2ln\u2061(x)+ln\u2061(y)<\/annotation><\/semantics><\/math>\u3092\u7c21\u7d04\u3057\u307e\u3059\u3002<\/li>\n\n\n\n
              2. x<\/mi>:<\/mo>e<\/mi>x<\/mi>\u2212<\/mo>3<\/mn>=<\/mo>10.<\/mn><\/mrow>x: ex\u22123=10.<\/annotation><\/semantics><\/math>\u3092\u89e3\u304d\u307e\u3059\u3002<\/li>\n\n\n\n
              3. x<\/mi>:<\/mo>l<\/mi>n<\/mi>\u2061<\/mtext>(<\/mo>2<\/mn>x<\/mi>)<\/mo>=<\/mo>5<\/mn><\/mrow>x: ln\u2061(2x)=5<\/annotation><\/semantics><\/math>\u3092\u89e3\u304d\u306a\u3055\u3044\u3002<\/li>\n<\/ol>\n\n\n\n
                \u30d1\u30fc\u30c8 B: \u30b0\u30e9\u30d5\u3068\u7279\u5fb4<\/h5>\n\n\n\n
                  \n
                1. f<\/mi>(<\/mo>x<\/mi>)<\/mo>=<\/mo>e<\/mi>x<\/mi>+<\/mo>4<\/mn><\/mrow>f(x)=ex+4<\/annotation><\/semantics><\/math>\u306e\u6c34\u5e73\u6f38\u8fd1\u7dda\u3092\u63cf\u304d\u306a\u3055\u3044\u3002<\/li>\n\n\n\n
                2. g<\/mi>(<\/mo>x<\/mi>)<\/mo>=<\/mo>l<\/mi>n<\/mi>\u2061<\/mtext>(<\/mo>x<\/mi>\u2212<\/mo>2<\/mn>)<\/mo><\/mrow>g(x)=ln\u2061(x\u22122)<\/annotation><\/semantics><\/math>\u306e x<\/mi>x<\/annotation><\/semantics><\/math> \u5207\u7247\u3092\u6c42\u3081\u306a\u3055\u3044\u3002(\u30d2\u30f3\u30c8: y<\/mi>=<\/mo>0<\/mn><\/mrow>y=0<\/annotation><\/semantics><\/math>\u3092\u8a2d\u5b9a\u3057\u3066e<\/mi>0<\/mn>=<\/mo>1<\/mn><\/mrow>e0=1<\/annotation><\/semantics><\/math>\u3092\u601d\u3044\u51fa\u3057\u306a\u3055\u3044\u3002)<\/li>\n<\/ol>\n\n\n\n
                  \u30d1\u30fc\u30c8 C: \u5fae\u7a4d\u5206<\/h5>\n\n\n\n
                    \n
                  1. y<\/mi>=<\/mo>3<\/mn>e<\/mi>2<\/mn>x<\/mi>\u2212<\/mo>4<\/mn>x<\/mi>2<\/mn><\/mrow>y=3e2x\u22124×2<\/annotation><\/semantics><\/math>\u3000\u306e\u5c0e\u95a2\u6570\u3092\u6c42\u3081\u306a\u3055\u3044\u3002<\/li>\n\n\n\n
                  2. x<\/mi>=<\/mo>5<\/mn><\/mrow>x=5<\/annotation><\/semantics><\/math>\u3068\u306a\u308b\u70b9\u306b\u304a\u3051\u308bf<\/mi>(<\/mo>x<\/mi>)<\/mo>=<\/mo>l<\/mi>n<\/mi>\u2061<\/mtext>(<\/mo>x<\/mi>)<\/mo><\/mrow>f(x)=ln\u2061(x)<\/annotation><\/semantics><\/math>\u66f2\u7dda\u306e\u50be\u304d\u3092\u6c42\u3081\u306a\u3055\u3044\u3002<\/li>\n\n\n\n
                  3. \u30c1\u30e3\u30ec\u30f3\u30b8:<\/strong> x<\/mi>=<\/mo>0<\/mn><\/mrow>x=0<\/annotation><\/semantics><\/math>\u3068\u306a\u308b\u70b9\u306b\u304a\u3051\u308b f<\/mi>(<\/mo>x<\/mi>)<\/mo>=<\/mo>e<\/mi>x<\/mi><\/mrow>f(x)=ex<\/annotation><\/semantics><\/math>\u3078\u306e\u63a5\u7dda\u306e\u65b9\u7a0b\u5f0f\u3092\u6c42\u3081\u306a\u3055\u3044\u3002<\/li>\n<\/ol>\n\n\n\n
                    \n\n\n\n

                    \u89e3\u7b54 (\u307e\u3068\u3081)<\/h4>\n\n\n\n
                      \n
                    • 1.<\/strong> l<\/mi>n<\/mi>\u2061<\/mtext>(<\/mo>x<\/mi>2<\/mn><\/msup>y<\/mi>)<\/mo><\/mrow>ln\u2061(x^2y)<\/annotation><\/semantics><\/math><\/li>\n\n\n\n
                    • 2.<\/strong>x<\/mi>=<\/mo>l<\/mi>n<\/mi>\u2061<\/mtext>(<\/mo>10<\/mn>)<\/mo>+<\/mo>3<\/mn>\u2248<\/mo>5.30<\/mn><\/mrow>x=ln\u2061(10)+3\u22485.30<\/annotation><\/semantics><\/math><\/li>\n\n\n\n
                    • 3.<\/strong> x<\/mi>=<\/mo>e<\/mi>5<\/mn><\/msup>2<\/mn><\/mfrac>\u2248<\/mo>74.21<\/mn><\/mrow>x = \\frac{e^5}{2} \u2248 74.21<\/annotation><\/semantics><\/math><\/li>\n\n\n\n
                    • 4.<\/strong> y<\/mi>=<\/mo>4<\/mn><\/mrow>y = 4<\/annotation><\/semantics><\/math><\/li>\n\n\n\n
                    • 5.<\/strong> 0<\/mn>=<\/mo>l<\/mi>n<\/mi>\u2061<\/mtext>(<\/mo>x<\/mi>\u2212<\/mo>2<\/mn>)<\/mo>\u2192<\/mo>e<\/mi>0<\/mn><\/msup>=<\/mo>x<\/mi>\u2212<\/mo>2<\/mn>\u2192<\/mo>1<\/mn>=<\/mo>x<\/mi>\u2212<\/mo>2<\/mn>\u2192<\/mo>x<\/mi>=<\/mo>3<\/mn><\/mrow>0=ln\u2061(x\u22122)\u2192e^0=x\u22122\u21921=x\u22122\u2192x=3<\/annotation><\/semantics><\/math>\u3002\u70b9\u306f (3,0)\u3002<\/li>\n\n\n\n
                    • 6.<\/strong> d<\/mi>y<\/mi><\/mrow>d<\/mi>x<\/mi><\/mrow><\/mfrac>=<\/mo>6<\/mn>e<\/mi>2<\/mn>x<\/mi><\/mrow><\/msup>\u2212<\/mo>8<\/mn>x<\/mi><\/mrow>\\frac{dy}{dx} = 6e^{2x} – 8x<\/annotation><\/semantics><\/math><\/li>\n\n\n\n
                    • 7.<\/strong> f<\/mi>\u2032<\/mtext>(<\/mo>x<\/mi>)<\/mo>=<\/mo>1<\/mn>x<\/mi><\/mfrac><\/mrow>f\u2032(x)=\\frac{1}{x}<\/annotation><\/semantics><\/math>\u3002 x<\/mi>=<\/mo>5<\/mn><\/mrow>x = 5<\/annotation><\/semantics><\/math>\u306b\u304a\u3044\u3066\u3001\u50be\u304d\u306f 1<\/mn>5<\/mn><\/mfrac>\\frac{1}{5}<\/annotation><\/semantics><\/math>\u307e\u305f\u306f 0.2\u3002<\/li>\n\n\n\n
                    • 8.<\/strong> f<\/mi>\u2032<\/mtext>(<\/mo>0<\/mn>)<\/mo>=<\/mo>e<\/mi>0<\/mn><\/msup>=<\/mo>1<\/mn><\/mrow>f\u2032(0)=e^0=1<\/annotation><\/semantics><\/math> (\u50be\u304d)\u3002 \u306b\u304a\u3044\u3066\u3001\u70b9\u306f (0,1). \u6b63\u63a5: y<\/mi>\u2212<\/mo>1<\/mn>=<\/mo>1<\/mn>(<\/mo>x<\/mi>\u2212<\/mo>0<\/mn>)<\/mo>\u2192<\/mo>y<\/mi>=<\/mo>x<\/mi>+<\/mo>1<\/mn><\/mrow>y\u22121=1(x\u22120)\u2192y=x+1<\/annotation><\/semantics><\/math>\u3002<\/li>\n<\/ul>\n\n\n\n
                      \n\n\n\n

                      <\/h3>\n","protected":false},"excerpt":{"rendered":"

                      \u7b2c4\u7ae0\uff1a\u6307\u6570\u95a2\u6570\u3068\u5bfe\u6570\u95a2\u6570 \u3053\u308c\u307e\u3067\u306e\u7ae0\u3067\u306f\u3001x2x^2 \u3084 x3x^3\u306e\u3088\u3046\u306a\u591a\u9805\u5f0f\u95a2\u6570\u306b\u7126\u70b9\u3092\u5f53\u3066\u3066\u304d\u307e\u3057\u305f\u3002\u7b2c4\u7ae0\u3067\u306f\u3001\u5909\u6570\u304c \u6307\u6570 \u3067\u3042\u308b\u95a2\u6570\u306b\u3064\u3044\u3066\u8003\u5bdf\u3057\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u95a2\u6570\u306f\u3001\u4eba\u53e3\u5897\u52a0\u3001\u653e\u5c04\u6027\u5d29\u58ca\u3001\u8907\u5229\u306e\u30e2\u30c7\u30eb\u5316\u306b\u4e0d\u53ef\u6b20\u3067\u3059\u3002 4.1 \u6307\u6570\u95a2\u6570\u3068\u6570ee \u6307\u6570\u95a2\u6570\u306f f(x)=axf(x)=a^x\u306e\u5f62\u3092\u3068\u308a\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u6570\u5b66\u7684\u624b\u6cd5\u3067\u306f\u3001\u4e3b\u306b \u81ea\u7136\u6307\u6570\u5e95 \u3067\u3042\u308b ee\u306b\u7126\u70b9\u3092\u5f53\u3066\u307e\u3059\u3002 4.2 \u5bfe\u6570\u95a2\u6570 \u5bfe\u6570\u306f\u6307\u6570\u95a2\u6570\u306e \u9006\u6570 \u3067\u3059\u3002y=exy=ex \u306a\u3089\u3070 x=ln\u2061(y)x=ln\u2061(y)\u3067\u3059\u3002 4.3 \u5bfe\u6570\u6cd5\u5247 ee\u304a\u3088\u3073 lnln\u3092\u542b\u3080\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u306b\u306f\u3001\u5bfe\u6570\u6cd5\u5247\u3092\u7fd2\u5f97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u6cd5\u5247\u306f\u5e95\u306b\u95a2\u308f\u3089\u305a\u540c\u3058\u3067\u3059\u304c\u3001\u81ea\u7136\u5bfe\u6570\u3067\u6700\u3082\u3088\u304f\u7528\u3044\u3089\u308c\u307e\u3059\u3002 4.4 exe^x\u3068ln(x)ln(x) \u306e\u5fae\u5206 \u5fae\u7a4d\u5206\u306f ee\u3092\u5e95\u3068\u3059\u308b\u5834\u5408\u306b\u975e\u5e38\u306b\u7c21\u6f54\u306b\u306a\u308a\u307e\u3059\u3002 4.5 \u7df4\u7fd2\u554f\u984c \u30d1\u30fc\u30c8 A: \u4ee3\u6570\u3068\u5bfe\u6570\u6cd5\u5247 \u30d1\u30fc\u30c8 B: \u30b0\u30e9\u30d5\u3068\u7279\u5fb4 \u30d1\u30fc\u30c8 C: \u5fae\u7a4d\u5206 \u89e3\u7b54 (\u307e\u3068\u3081)<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8],"tags":[],"class_list":["post-1155","post","type-post","status-publish","format-standard","hentry","category-math"],"_links":{"self":[{"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/posts\/1155","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1155"}],"version-history":[{"count":7,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/posts\/1155\/revisions"}],"predecessor-version":[{"id":1258,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=\/wp\/v2\/posts\/1155\/revisions\/1258"}],"wp:attachment":[{"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1155"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1155"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/archive4ones.com\/2ndstudy\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1155"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}