Question

question
what is the value of $log_{5}sqrt5{25}$?
answer

Explanation:

Step1: Rewrite root as exponent

$\log_{5} 25^{\frac{1}{5}}$

Step2: Express 25 as power of 5

$\log_{5} (5^2)^{\frac{1}{5}}$

Step3: Simplify exponent of 5

$\log_{5} 5^{\frac{2}{5}}$

Step4: Apply log power rule

$\frac{2}{5} \log_{5} 5$

Step5: Evaluate $\log_{5}5$

$\frac{2}{5} \times 1$

Answer:

$\frac{2}{5}$