Precalculus Examples

$\frac{1}{5 \log_{6} (x) + \log_{6} (7) - \log_{6} (y)}$

Step 1

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

$\frac{1}{\log_{6} (x^{5}) + \log_{6} (7) - \log_{6} (y)}$

Step 2

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

$\frac{1}{\log_{6} (x^{5} \cdot 7) - \log_{6} (y)}$

Step 3

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

$\frac{1}{\log_{6} (\frac{x^{5} \cdot 7}{y})}$

Step 4

Move $7$ to the left of $x^{5}$ .

$\frac{1}{\log_{6} (\frac{7 x^{5}}{y})}$