Simplify/Condense log base 6 of 3- log base 6 of 6

$\log_{6} (3) - \log_{6} (6)$

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

$\log_{6} (\frac{3}{6})$

Cancel the common factor of $3$ and $6$ .

Factor $3$ out of $3$ .

$\log_{6} (\frac{3 (1)}{6})$

Cancel the common factors.

Factor $3$ out of $6$ .

$\log_{6} (\frac{3 \cdot 1}{3 \cdot 2})$

Cancel the common factor.

$\log_{6} (\frac{3 \cdot 1}{3 \cdot 2})$

Rewrite the expression.

$\log_{6} (\frac{1}{2})$

The result can be shown in multiple forms.

Exact Form:

$\log_{6} (\frac{1}{2})$

Decimal Form:

$- 0.38685280 \dots$