Simplify log base 2 of cube root of 16

$\log_{2} (\sqrt[3]{16})$

Step 1

Rewrite $16$ as $2^{3} \cdot 2$ .

Factor $8$ out of $16$ .

$\log_{2} (\sqrt[3]{8 (2)})$

Rewrite $8$ as $2^{3}$ .

$\log_{2} (\sqrt[3]{2^{3} \cdot 2})$

$\log_{2} (\sqrt[3]{2^{3} \cdot 2})$

Step 2

Pull terms out from under the radical.

$\log_{2} (2 \sqrt[3]{2})$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\log_{2} (2 \sqrt[3]{2})$

Decimal Form:

$1.\overline{3}$

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