Simplify/Condense log base 6 of 3+ log base 6 of 8- log base 6 of 4

$\log_{6} (3) + \log_{6} (8) - \log_{6} (4)$

Step 1

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

$\log_{6} (3 \cdot 8) - \log_{6} (4)$

Step 2

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

$\log_{6} (\frac{3 \cdot 8}{4})$

Step 3

Cancel the common factor of $8$ and $4$ .

Factor $4$ out of $3 \cdot 8$ .

$\log_{6} (\frac{4 (3 \cdot 2)}{4})$

Cancel the common factors.

Factor $4$ out of $4$ .

$\log_{6} (\frac{4 (3 \cdot 2)}{4 (1)})$

Cancel the common factor.

$\log_{6} (\frac{4 (3 \cdot 2)}{4 \cdot 1})$

Rewrite the expression.

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

Divide $3 \cdot 2$ by $1$ .

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

Step 4

Multiply $3$ by $2$ .

$\log_{6} (6)$

Step 5

Logarithm base $6$ of $6$ is $1$ .

$1$