Simplify/Condense log base 5 of 8- log base 5 of 12

$\log_{5} (8) - \log_{5} (12)$

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

$\log_{5} (\frac{8}{12})$

Cancel the common factor of $8$ and $12$ .

Factor $4$ out of $8$ .

$\log_{5} (\frac{4 (2)}{12})$

Cancel the common factors.

Factor $4$ out of $12$ .

$\log_{5} (\frac{4 \cdot 2}{4 \cdot 3})$

Cancel the common factor.

$\log_{5} (\frac{4 \cdot 2}{4 \cdot 3})$

Rewrite the expression.

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$- 0.25192963 \dots$