Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

Multiply $- 1$ by $- 4$ .

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

Step 1.4

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

$- 2 + 4 - 2$

Step 2

Simplify by adding and subtracting.

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Step 2.1

Add $- 2$ and $4$ .

$2 - 2$

Step 2.2

Subtract $2$ from $2$ .

$0$