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

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

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

Cancel the common factors.

Factor $3$ out of $6$ .

$\log_{4} (\frac{3 \cdot 8}{3 \cdot 2})$

Cancel the common factor.

$\log_{4} (\frac{3 \cdot 8}{3 \cdot 2})$

Rewrite the expression.

$\log_{4} (\frac{8}{2})$

Step 4

Cancel the common factor of $8$ and $2$ .

Factor $2$ out of $8$ .

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

Cancel the common factors.

Factor $2$ out of $2$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\log_{4} (\frac{4}{1})$

Divide $4$ by $1$ .

$\log_{4} (4)$

Step 5

Logarithm base $4$ of $4$ is $1$ .

$1$