Precalculus Examples

$5^{\log_{5} (x^{4}) - 6 \log_{5} (y)}$

Step 1

Simplify $- 6 \log_{5} (y)$ by moving $6$ inside the logarithm.

$5^{\log_{5} (x^{4}) - \log_{5} (y^{6})}$

Step 2

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

$5^{\log_{5} (\frac{x^{4}}{y^{6}})}$

Step 3

Exponentiation and log are inverse functions.

$\frac{x^{4}}{y^{6}}$