Simplify/Condense 3 log base 2 of 8+4 log base 2 of 1/2- log base 3 of 2

$3 \log_{2} (8) + 4 \log_{2} (\frac{1}{2}) - \log_{3} (2)$

Step 1

Simplify each term.

Logarithm base $2$ of $8$ is $3$ .

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

Multiply $3$ by $3$ .

$9 + 4 \log_{2} (\frac{1}{2}) - \log_{3} (2)$

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

$9 + 4 \cdot - 1 - \log_{3} (2)$

Multiply $4$ by $- 1$ .

$9 - 4 - \log_{3} (2)$

Step 2

Subtract $4$ from $9$ .

$5 - \log_{3} (2)$

Step 3

The result can be shown in multiple forms.

Exact Form:

$5 - \log_{3} (2)$

Decimal Form:

$4.36907024 \dots$