Simplify/Condense log of 8-2 log of 6+ log of 3

$\log (8) - 2 \log (6) + \log (3)$

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

$\log (8 \cdot 3) - 2 \log (6)$

Simplify each term.

Multiply $8$ by $3$ .

$\log (24) - 2 \log (6)$

Simplify $- 2 \log (6)$ by moving $2$ inside the logarithm.

$\log (24) - \log (6^{2})$

Raise $6$ to the power of $2$ .

$\log (24) - \log (36)$

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

$\log (\frac{24}{36})$

Cancel the common factor of $24$ and $36$ .

Factor $12$ out of $24$ .

$\log (\frac{12 (2)}{36})$

Cancel the common factors.

Factor $12$ out of $36$ .

$\log (\frac{12 \cdot 2}{12 \cdot 3})$

Cancel the common factor.

$\log (\frac{12 \cdot 2}{12 \cdot 3})$

Rewrite the expression.

$\log (\frac{2}{3})$

The result can be shown in multiple forms.

Exact Form:

$\log (\frac{2}{3})$

Decimal Form:

$- 0.17609125 \dots$