Evaluate log base 3 of 27+ log base 1/16 of 2

$\log_{3} (27) + \log_{\frac{1}{16}} (2)$

Simplify each term.

Logarithm base $3$ of $27$ is $3$ .

$3 + \log_{\frac{1}{16}} (2)$

Logarithm base $\frac{1}{16}$ of $2$ is $- \frac{1}{4}$ .

$3 - \frac{1}{4}$

To write $3$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$3 \cdot \frac{4}{4} - \frac{1}{4}$

Combine $3$ and $\frac{4}{4}$ .

$\frac{3 \cdot 4}{4} - \frac{1}{4}$

Combine the numerators over the common denominator.

$\frac{3 \cdot 4 - 1}{4}$

Simplify the numerator.

Multiply $3$ by $4$ .

$\frac{12 - 1}{4}$

Subtract $1$ from $12$ .

$\frac{11}{4}$

The result can be shown in multiple forms.

Exact Form:

$\frac{11}{4}$

Decimal Form:

$2.75$

Mixed Number Form:

$2 \frac{3}{4}$