Simplify/Condense 3* log base 4 of 8-5* log base 4 of 2

$3 \cdot \log_{4} (8) - 5 \cdot \log_{4} (2)$

Step 1

Simplify each term.

Logarithm base $4$ of $8$ is $\frac{3}{2}$ .

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

Multiply $3 (\frac{3}{2})$ .

Combine $3$ and $\frac{3}{2}$ .

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

Multiply $3$ by $3$ .

$\frac{9}{2} - 5 \cdot \log_{4} (2)$

Logarithm base $4$ of $2$ is $\frac{1}{2}$ .

$\frac{9}{2} - 5 \cdot \frac{1}{2}$

Combine $- 5$ and $\frac{1}{2}$ .

$\frac{9}{2} + \frac{- 5}{2}$

Move the negative in front of the fraction.

$\frac{9}{2} - \frac{5}{2}$

Step 2

Combine fractions.

Combine the numerators over the common denominator.

$\frac{9 - 5}{2}$

Simplify the expression.

Subtract $5$ from $9$ .

$\frac{4}{2}$

Divide $4$ by $2$ .

$2$