Precalculus Examples

$5 \log_{2} (y - 7) - 3 \log_{2} (y + 8)$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Simplify $5 \log_{2} (y - 7)$ by moving $5$ inside the logarithm.

$\log_{2} ({(y - 7)}^{5}) - 3 \log_{2} (y + 8)$

Step 1.2

Simplify $- 3 \log_{2} (y + 8)$ by moving $3$ inside the logarithm.

$\log_{2} ({(y - 7)}^{5}) - \log_{2} ({(y + 8)}^{3})$

Step 2

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

$\log_{2} (\frac{{(y - 7)}^{5}}{{(y + 8)}^{3}})$