Question

question
what is the value of $log_{2}sqrt5{2}$?
answer attempt 1 out of 2

Explanation:

Step1: Rewrite root as exponent

$\sqrt[5]{2} = 2^{\frac{1}{5}}$

Step2: Apply logarithm power rule

$\log_{2}2^{\frac{1}{5}} = \frac{1}{5}\log_{2}2$

Step3: Evaluate $\log_{2}2$

$\log_{2}2 = 1$, so $\frac{1}{5} \times 1 = \frac{1}{5}$

Answer:

$\frac{1}{5}$