Question

y=(1/5)^x
y=10^x
y=1,3^x
y=0,4^x
Чем равен x?

Answer 1

Ответ:

$y = ( \frac{1}{5} )^{x} \\ ( \frac{1}{5} ) ^{x} = y \\ log_{ \frac{1}{5} }(( \frac{1}{5}) ^{x} ) = log_{ \frac{1}{5} }(y) \\ x = log_{ - 5}(y)$

$y = {10}^{x} \\ {10}^{x} = y \\ log_{10}( {10}^{x} ) = log_{10}(y) \\ x = log_{10}(y)$

$y = {1.3}^{x} \\ ( \frac{13}{10} ) ^{x} = y \\ log_{ \frac{13}{10} }( ( \frac{13}{10} ^{x}) ) = log_{ \frac{13}{10} }(y) \\ x = log_{ \frac{13}{10} }(y)$

$y = {0.4}^{x} \\ (\frac{2}{5} ) ^{x} = y \\ log_{ \frac{2}{5} }(( \frac{2}{5}) ^{x} ) = log_{ \frac{2}{5} }(y) \\ x = log_{ \frac{2}{5} }(y)$

Формула, которую используем:

$log_{a}( {a}^{x} ) = x$