Precalculus Examples

$\log_{5} ({(5 x)}^{3})$

Step 1

Expand $\log_{5} ({(5 x)}^{3})$ by moving $3$ outside the logarithm.

$3 \log_{5} (5 x)$

Step 2

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

$3 (\log_{5} (5) + \log_{5} (x))$

Step 3

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

$3 (1 + \log_{5} (x))$

Step 4

Apply the distributive property.

$3 \cdot 1 + 3 \log_{5} (x)$

Step 5

Multiply $3$ by $1$ .

$3 + 3 \log_{5} (x)$