Write as a Single Logarithm 5 log of 2-2 log of 2

$5 \log (2) - 2 \log (2)$

Simplify each term.

Simplify $5 \log (2)$ by moving $5$ inside the logarithm.

$\log (2^{5}) - 2 \log (2)$

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

$\log (32) - 2 \log (2)$

Simplify $- 2 \log (2)$ by moving $2$ inside the logarithm.

$\log (32) - \log (2^{2})$

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

$\log (32) - \log (4)$

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\log (\frac{32}{4})$

Divide $32$ by $4$ .

$\log (8)$

The result can be shown in multiple forms.

Exact Form:

$\log (8)$

Decimal Form:

$0.90308998 \dots$