Precalculus Examples

$\log_{5} (8 x^{3})$

Step 1

Rewrite $\log_{5} (8 x^{3})$ as $\log_{5} (8) + \log_{5} (x^{3})$ .

$\log_{5} (8) + \log_{5} (x^{3})$

Step 2

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

$\log_{5} (8) + 3 \log_{5} (x)$

Step 3

Simplify each term.

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Step 3.1

Rewrite $\log_{5} (8)$ as $\log_{5} (2^{3})$ .

$\log_{5} (2^{3}) + 3 \log_{5} (x)$

Step 3.2

Expand $\log_{5} (2^{3})$ by moving $3$ outside the logarithm.

$3 \log_{5} (2) + 3 \log_{5} (x)$