何度も解いて体で覚えましょう!
指数関数 y=2^x について,x が以下の値をとるときの y の値を求めよ。
【解答】
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}} \newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}} \newcommand\colBX[2]{\colorbox{#1}{#2}} \begin{align*} &\colMM{orange}{マイナス乗は}\\ y &= 2^{-2}\\ & \colMM{orange}{\Darr 逆数に}\\ &= \dfrac{1}{2^2} = \dfrac{1}{4} = 0.25 \end{align*}
【解答】
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}} \newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}} \newcommand\colBX[2]{\colorbox{#1}{#2}} \begin{align*} &\colMM{orange}{マイナス乗は}\\ y &= 2^{-1.5}\\ & \colMM{orange}{\Darr 逆数に}\\ &= \dfrac{1}{2^{1.5}}\\ & \colMM{green}{\Darr 小数は分数に}\\ &= \dfrac{1}{2^{\frac32}}\\ & \colMM{green}{\Darr 分数乗は\sqrt{ルート}に}\\ &= \dfrac{1}{\sqrt[2]{2^3}}\\ \\ &= \dfrac{1}{2\sqrt{2}} = \dfrac{\sqrt{2}}{4} \fallingdotseq \dfrac{1.4}{4} = 0.35 \end{align*}
【解答】
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}} \newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}} \newcommand\colBX[2]{\colorbox{#1}{#2}} \begin{align*} &\colMM{orange}{マイナス乗は}\\ y &= 2^{-1}\\ & \colMM{orange}{\Darr 逆数に}\\ &= \dfrac{1}{2^1} = \dfrac{1}{2} = 0.5 \end{align*}
【解答】
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}} \newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}} \newcommand\colBX[2]{\colorbox{#1}{#2}} \begin{align*} &\colMM{orange}{マイナス乗は}\\ y &= 2^{-0.5}\\ & \colMM{orange}{\Darr 逆数に}\\ &= \dfrac{1}{2^{0.5}}\\ & \colMM{green}{\Darr 小数は分数に}\\ &= \dfrac{1}{2^{\frac12}}\\ & \colMM{green}{\Darr 分数乗は\sqrt{ルート}に}\\ &= \dfrac{1}{\sqrt[2]{2^1}}\\ \\ &= \dfrac{1}{\sqrt{2}} = \dfrac{\sqrt{2}}{2} \fallingdotseq \dfrac{1.4}{2} = 0.7 \end{align*}
【解答】
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}} \newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}} \newcommand\colBX[2]{\colorbox{#1}{#2}} \begin{align*} &\colMM{orange}{0乗は}\\ y &= 2^{0}\\ &= \colBX{bisque}{$1$} \end{align*}
【解答】
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}} \newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}} \newcommand\colBX[2]{\colorbox{#1}{#2}} \begin{align*} y &= 2^{0.5}\\ & \colMM{green}{\Darr 小数は分数に}\\ &= 2^{\frac12}\\ & \colMM{green}{\Darr 分数乗は\sqrt{ルート}に}\\ &= \sqrt[2]{2^1}\\ \\ &= \sqrt{2} \fallingdotseq 1.4 \end{align*}
【解答】
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}} \newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}} \newcommand\colBX[2]{\colorbox{#1}{#2}} \begin{align*} y &= 2^{1} = 2\\ \end{align*}
【解答】
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}} \newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}} \newcommand\colBX[2]{\colorbox{#1}{#2}} \begin{align*} y &= 2^{1.5}\\ & \colMM{green}{\Darr 小数は分数に}\\ &= 2^{\frac32}\\ & \colMM{green}{\Darr 分数乗は\sqrt{ルート}に}\\ &= \sqrt[2]{2^3}\\ \\ &= 2\sqrt{2} \fallingdotseq 2 \times 1.4 = 2.8 \end{align*}
【解答】
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}} \newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}} \newcommand\colBX[2]{\colorbox{#1}{#2}} \begin{align*} y &= 2^{2} = 4\\ \end{align*}
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