Precalculus Examples

$\log_{x} (\frac{1}{x^{2}})$

Step 1

Rewrite $\log_{x} (\frac{1}{x^{2}})$ as $\log_{x} (1) - \log_{x} (x^{2})$ .

$\log_{x} (1) - \log_{x} (x^{2})$

Step 2

Expand $\log_{x} (x^{2})$ by moving $2$ outside the logarithm.

$\log_{x} (1) - (2 \log_{x} (x))$

Step 3

Logarithm base $x$ of $1$ is $0$ .

$0 - (2 \log_{x} (x))$

Step 4

Logarithm base $x$ of $x$ is $1$ .

$0 - (2 \cdot 1)$

Step 5

Multiply $2$ by $1$ .

$0 - 1 \cdot 2$

Step 6

Multiply $- 1$ by $2$ .

$0 - 2$

Step 7

Subtract $2$ from $0$ .

$- 2$