Precalculus Examples

$\log (5) + 2 \log (x) - \log (y)$

Step 1

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$2 \log (x) + \log (\frac{5}{y})$

Step 2

Simplify $2 \log (x)$ by moving $2$ inside the logarithm.

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

Step 3

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

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

Step 4

Combine $x^{2}$ and $\frac{5}{y}$ .

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

Step 5

Move $5$ to the left of $x^{2}$ .

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