Precalculus Examples

$4 \log_{5} (x + 5) - \log_{5} (x - 8) - \log_{5} (x - 4)$

Step 1

Simplify $4 \log_{5} (x + 5)$ by moving $4$ inside the logarithm.

$\log_{5} ({(x + 5)}^{4}) - \log_{5} (x - 8) - \log_{5} (x - 4)$

Step 2

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

$\log_{5} (\frac{{(x + 5)}^{4}}{x - 8}) - \log_{5} (x - 4)$

Step 3

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

$\log_{5} (\frac{\frac{{(x + 5)}^{4}}{x - 8}}{x - 4})$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\log_{5} (\frac{{(x + 5)}^{4}}{x - 8} \cdot \frac{1}{x - 4})$

Step 5

Multiply $\frac{{(x + 5)}^{4}}{x - 8}$ by $\frac{1}{x - 4}$ .

$\log_{5} (\frac{{(x + 5)}^{4}}{(x - 8) (x - 4)})$