Precalculus Examples

$\log_{6} (\frac{5 x^{3}}{6})$

Step 1

Rewrite $\log_{6} (\frac{5 x^{3}}{6})$ as $\log_{6} (5 x^{3}) - \log_{6} (6)$ .

$\log_{6} (5 x^{3}) - \log_{6} (6)$

Step 2

Logarithm base $6$ of $6$ is $1$ .

$\log_{6} (5 x^{3}) - 1 \cdot 1$

Step 3

Multiply $- 1$ by $1$ .

$\log_{6} (5 x^{3}) - 1$

Step 4

Rewrite $\log_{6} (5 x^{3})$ as $\log_{6} (5) + \log_{6} (x^{3})$ .

$\log_{6} (5) + \log_{6} (x^{3}) - 1$

Step 5

Expand $\log_{6} (x^{3})$ by moving $3$ outside the logarithm.

$\log_{6} (5) + 3 \log_{6} (x) - 1$