Question

log x na base 2 + log x na base raiz de 2 = -3

Answer 1

$log_{2} x+log_{ \sqrt{2} } x=-3$

$log_{2} x+ \dfrac{log_{ 2 } x}{log_{ 2 } \sqrt{2}} =-3$

$log_{2} x+ \dfrac{log_{ 2 } x}{log_{ 2 } 2^{ \frac{1}{2} } } =-3$

$log_{2} x+ \dfrac{log_{ 2 } x}{ \frac{1}{2} .log_{ 2 } 2} =-3$

$log_{2} x+ \dfrac{log_{ 2 } x}{ \frac{1}{2} .1} =-3$

$log_{2} x+ \dfrac{log_{ 2 } x}{ \frac{1}{2} } =-3$

$log_{2} x+ 2log_{ 2 } x =-3$

$3log_{ 2 } x =-3$

$log_{ 2 } x =-1$

$x= 2^{-1}$

$x= \dfrac{1}{2}$