Precalculus Examples

$\log_{5} (\frac{5 x^{2}}{y})$

Step 1

Rewrite $\log_{5} (\frac{5 x^{2}}{y})$ as $\log_{5} (5 x^{2}) - \log_{5} (y)$ .

$\log_{5} (5 x^{2}) - \log_{5} (y)$

Step 2

Rewrite $\log_{5} (5 x^{2})$ as $\log_{5} (5) + \log_{5} (x^{2})$ .

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

Step 3

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

$\log_{5} (5) + 2 \log_{5} (x) - \log_{5} (y)$

Step 4

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

$1 + 2 \log_{5} (x) - \log_{5} (y)$