Simplify/Condense log base 3 of 5+5 log base 3 of 2

$\log_{3} (5) + 5 \log_{3} (2)$

Simplify each term.

Simplify $5 \log_{3} (2)$ by moving $5$ inside the logarithm.

$\log_{3} (5) + \log_{3} (2^{5})$

Raise $2$ to the power of $5$ .

$\log_{3} (5) + \log_{3} (32)$

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\log_{3} (5 \cdot 32)$

Multiply $5$ by $32$ .

$\log_{3} (160)$

The result can be shown in multiple forms.

Exact Form:

$\log_{3} (160)$

Decimal Form:

$4.61962228 \dots$