Задание 4.1

1) ${\log <!--\; FUNCTION\; APPLICATION\; -->}_7\frac{1}{49}=-3$
$7^{-3}=\frac{1}{49}$
$7^{-3}\ne 7^{-2}$Нет

2) ${\log <!--\; FUNCTION\; APPLICATION\; -->}_{25}5=2$
$25^2\ne 5;$Нет

3) ${\log <!--\; FUNCTION\; APPLICATION\; -->}_{5}125=\frac{1}{3}$
$5^{\frac{1}{3}}=125$
$5^{\frac{1}{3}}\ne 5^3$ Нет

4) ${\log <!--\; FUNCTION\; APPLICATION\; -->}_3\frac{1}{81}=-4$
$\begin{array}{ccc}\hfill 3^{-4}& =\frac{1}{81}\hfill & \hfill \\ \hfill \frac{1}{81}& =\frac{1}{81}\hfill \end{array}$Да

5)${\log <!--\; FUNCTION\; APPLICATION\; -->}_{0,01}10=2$
$0,01^2=10$
$0,0001\ne 10$Нет

6) $\lg <!--\; FUNCTION\; APPLICATION\; -->0,0001=-4$;
$10^{-4}=0,0001$
$0,0001=0,0001$ Да

7) ${\log <!--\; FUNCTION\; APPLICATION\; -->}_{\frac{1}{9}}3\sqrt{3}=\frac{2}{3}$
${\left(\frac{1}{9}\right)}^{\frac{2}{3}}=3\sqrt[3]{3^1}$
${(\sqrt[3]{9})}^2=\sqrt[3]{3^3\cdot 3}$
$\sqrt[3]{9^2}=\sqrt[3]{9^2}$Да

8) ${\log <!--\; FUNCTION\; APPLICATION\; -->}_{\sqrt{5}}0,2=-2$
${(\sqrt{5})}^{-2}=0,2$
${\left(5^{\frac{1}{2}}\right)}^{-2}=0,2$
$5^{-1}=5^{-1}$Да