Algebra Examples

$\log_{5} ({(5 x)}^{- 5})$

Step 1

Expand $\log_{5} ({(5 x)}^{- 5})$ by moving $- 5$ outside the logarithm.

$- 5 \log_{5} (5 x)$

Step 2

Rewrite $\log_{5} (5 x)$ as $\log_{5} (5) + \log_{5} (x)$ .

$- 5 (\log_{5} (5) + \log_{5} (x))$

Step 3

Logarithm base $5$ of $5$ is $1$ .

$- 5 (1 + \log_{5} (x))$

Step 4

Apply the distributive property.

$- 5 \cdot 1 - 5 \log_{5} (x)$

Step 5

Multiply $- 5$ by $1$ .

$- 5 - 5 \log_{5} (x)$