演習問題

${\displaystyle {log}_{3}27}$

${\displaystyle {log}_2\left(\frac{1}{\sqrt{8}}\right)}$

次の式のグラフを描け．

${\displaystyle y={log}_{2}x}$

次の式のグラフを描け．

${\displaystyle y={log}_{\frac{1}{2}}x}$

次の対数方程式を解け．

${\displaystyle {log}_3(x-1)={log}_9(x+1)}$

次の対数方程式を解け．

${\displaystyle {log}_2(x+3)+{log}_2(x-4)=3}$

次の対数不等式を解け．

${\displaystyle {log}_2(x+2)+{log}_{2}x<3}$

次の問題を微分せよ．

${\displaystyle y=4^x}$

次の問題を微分せよ．

${\displaystyle y=\frac{{\left(5x+1\right)}^5}{{\left(x^3-4\right)}^4}}$

次の極限を求めよ．

${\displaystyle \underset{x\to \infty }{\lim }\left\{x\log \left(x+1\right)-x\log x\right\}}$

次の指数方程式を解け．

${\displaystyle 2^x=3^{x-1}}$

次の指数方程式を解け．

${\displaystyle 2^x+2^{-x}=5}$

次の指数不等式を解け．

${\displaystyle 3^{2x+1}>27\cdot {\left(\frac{1}{\sqrt{3}}\right)}^{2x}}$

次の指数不等式を解け．

${\displaystyle 3^{x+1}<2^{2x-1}}$

${\displaystyle {log}_{\frac{1}{2}}32}$

次の式を簡単にせよ．

${\displaystyle {log}_{6}18+{log}_{6}12}$

次の式を簡単にせよ．

${\displaystyle {\text{log}}_{\text{2}}81·{\text{log}}_{\text{3}}2}$

次の式を簡単にせよ．

${\displaystyle {log}_9\sqrt[\text{4}]{\text{3}}+{log}_{\frac{1}{3}}9}$

次の式を簡単にせよ．

${\displaystyle {log}_{2}64÷{log}_{3}27}$

次の式を簡単にせよ．

${\displaystyle log{e}^2+log\frac{1}{e}+log\frac{1}{\sqrt{e}}}$

次の式を簡単にせよ．

${\displaystyle {log}_{8}125-{log}_{4}10-{log}_2\left(\frac{1}{\sqrt{10}}\right)}$

次の式を簡単にせよ

${\displaystyle {log}_{\sqrt{3}}8+{log}_{2}3{log}_{9}4+{log}_{\frac{1}{3}}16}$

次の対数方程式を解け．

${\displaystyle {log}_{5}2x=-1}$ 

次の対数不等式を解け．

${\displaystyle {log}_2(x-1)+{log}_{4}2<0}$

次の対数不等式を解け

${\displaystyle {log}_{3}9\cdot {log}_{\frac{1}{3}}4\leqq {log}_{9}x\leqq {log}_{\frac{1}{3}}4+{log}_{3}2}$

次の不等式を解け

${\displaystyle {\left({log}_{3}x\right)}^2-5{log}_{3}9x<-4}$

${\displaystyle 3^{50}}$ は何桁の数か求めよ．ただし， ${\displaystyle {log}_{10}3=0.4771}$ である．

 ${\displaystyle 3^{50}}$ の最上位の数を求めよ．ただし，下の常用対数の値を用いてよい．

${\displaystyle {log}_{10}1=0}$，${\displaystyle {log}_{10}6=0.7782}$，${\displaystyle {log}_{10}2=0.3010}$，${\displaystyle {log}_{10}7=0.8451}$，${\displaystyle {log}_{10}3=0.4771}$，${\displaystyle {log}_{10}8=0.9031}$，${\displaystyle {log}_{10}4=0.6021}$，${\displaystyle {log}_{10}9=0.9542}$，${\displaystyle {log}_{10}5=0.6990}$，${\displaystyle {log}_{10}10=1}$

次のことを証明せよ．

${\displaystyle z=log\sqrt{x^2+y^2}}$ ならば ${\displaystyle {\left(\frac{\partial z}{\partial x}\right)}^2+{\left(\frac{\partial z}{\partial y}\right)}^2=\frac{1}{e^{2z}}}$ である．

次の問題を積分せよ（不定積分）．

${\displaystyle {\displaystyle \int \tan xdx}}$