Write as a Single Logarithm 6* log base 4 of 2- log base 4 of 8

$6 \cdot \log_{4} (2) - \log_{4} (8)$

Step 1

Simplify each term.

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

$6 \cdot \frac{1}{2} - \log_{4} (8)$

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

$3 - \frac{3}{2}$

Step 2

To write $3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$3 \cdot \frac{2}{2} - \frac{3}{2}$

Step 3

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

$\frac{3 \cdot 2}{2} - \frac{3}{2}$

Step 4

Combine the numerators over the common denominator.

$\frac{3 \cdot 2 - 3}{2}$

Step 5

Simplify the numerator.

Multiply $3$ by $2$ .

$\frac{6 - 3}{2}$

Subtract $3$ from $6$ .

$\frac{3}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{2}$

Decimal Form:

$1.5$

Mixed Number Form:

$1 \frac{1}{2}$