Question

log root5 to the base cubeth root 5​

Answer 1

$\huge \boxed{ \red{\mathfrak{solution}}}$

To find the value of

$log_{ \sqrt[3]{5} }( \sqrt{5} )$

We have to use the formula :

$\boxed{ \bold{log_{ {a}^{x} }( {b}^{y} ) = \frac{y}{x} log_{a}(b) }}$

and

$\boxed{ \bold{log_{a}(a) = 1}}$

$\rightarrow log_{ \sqrt[3]{5} }( \sqrt{5} ) \\ \\ \rightarrow \: log_{ {5}^{ \frac{1}{3} } }( {5}^{ \frac{1}{2} } ) \\ \\ \rightarrow \: \frac{1}{2} \times \frac{3}{1} log_{5}(5) \\ \\ \rightarrow \: \frac{3}{2 } \times 1 \\ \\ \rightarrow \: \frac{3}{2}$

Hence the value is

$\huge \boxed{ \bold{ \blue{\mathfrak{ \frac{3}{2}}} }}$