Evaluate log base 5 of 1/25- log base 2 of 1/16+ log base 9 of 1/81

$\log_{5} (\frac{1}{25}) - \log_{2} (\frac{1}{16}) + \log_{9} (\frac{1}{81})$

Simplify each term.

Logarithm base $5$ of $\frac{1}{25}$ is $- 2$ .

$- 2 - \log_{2} (\frac{1}{16}) + \log_{9} (\frac{1}{81})$

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

$- 2 - - 4 + \log_{9} (\frac{1}{81})$

Multiply $- 1$ by $- 4$ .

$- 2 + 4 + \log_{9} (\frac{1}{81})$

Logarithm base $9$ of $\frac{1}{81}$ is $- 2$ .

$- 2 + 4 - 2$

Simplify by adding and subtracting.

Add $- 2$ and $4$ .

$2 - 2$

Subtract $2$ from $2$ .

$0$