Question

Evaluate the log without a calculator ( Show your work )

$log_{2} \sqrt[5]{16}$

Answer 1

Answer: x = 1/5

//Hope it helps.

Answer 2

Answer:

$\log_2(\sqrt[5]{16} )=\frac{4}{5}$

Step-by-step explanation:

The given logarithmic expression is:

$\log_2(\sqrt[5]{16} )$

We rewrite the radical as an exponent to obtain;

$\log_2(\sqrt[5]{16} )=\log_2(16^{\frac{1}{5}} )$

Recall and use the power rule; $\log_a(M^n)=n\log_a(M)$

$\log_2(\sqrt[5]{16} )=\frac{1}{5}\log_2(16 )$

We write 16 as an index number to base 2.

$\log_2(\sqrt[5]{16} )=\frac{1}{5}\log_2(2^4)$

We apply the power rule again;

$\log_2(\sqrt[5]{16} )=\frac{4}{5}\log_2(2)$

We simplify to get;

$\log_2(\sqrt[5]{16} )=\frac{4}{5}(1)$

$\log_2(\sqrt[5]{16} )=\frac{4}{5}$