Precalculus Examples

$\frac{\log (x^{2})}{\log (10 y^{3})}$

Step 1

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

$\frac{2 \log (x)}{\log (10 y^{3})}$

Step 2

Rewrite $\log (10 y^{3})$ as $\log (10) + \log (y^{3})$ .

$\frac{2 \log (x)}{\log (10) + \log (y^{3})}$

Step 3

Expand $\log (y^{3})$ by moving $3$ outside the logarithm.

$\frac{2 \log (x)}{\log (10) + 3 \log (y)}$

Step 4

Logarithm base $10$ of $10$ is $1$ .

$\frac{2 \log (x)}{1 + 3 \log (y)}$