Question

log:5 $\sqrt[5]{5}$

Answer 1

$\text{log}_{\sqrt[5]{5}}~5=x~~\Rightarrow~~5^{x}=\sqrt[5]{5}$

$5^{x}=\sqrt[5]{5}$

$5^{x}=5^{\frac{1}{5}}$

$x=\dfrac{1}{5}$

Answer 2

$log ( 5* \sqrt[5]{5} ) = log ( 5* \ 5^{1/5} ) = log ( 5^{6/5} )$

por definição:

$log ( 5^{6/5} ) = log_{10} ( 5^{6/5} )$
$10^n=5^{6/5}$


$10^n=5^{6/5}$
$log(10^n)=log (5^{6/5})$
$n*log(10) = 6/5*log(5)$
$n*1 = 6/5 *log (5)$$[/tex] [tex]n= 6/5* log(5)$