Algebra Examples

\frac{1}{3} (log (x) - log (y))

$\frac{1}{3} (\log (x) - \log (y))$

Step 1

Use the quotient property of logarithms,

{log}_{b} (x) - {log}_{b} (y) = {log}_{b} (\frac{x}{y})

$\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

\frac{1}{3} \cdot log (\frac{x}{y})

$\frac{1}{3} \cdot \log (\frac{x}{y})$

Step 2

Simplify

\frac{1}{3} log (\frac{x}{y})

$\frac{1}{3} \log (\frac{x}{y})$ by moving

\frac{1}{3}

$\frac{1}{3}$ inside the logarithm.

log ({(\frac{x}{y})}^{\frac{1}{3}})

$\log ({(\frac{x}{y})}^{\frac{1}{3}})$

Step 3

Apply the product rule to

\frac{x}{y}

$\frac{x}{y}$ .

log (\frac{x^{\frac{1}{3}}}{y^{\frac{1}{3}}})

$\log (\frac{x^{\frac{1}{3}}}{y^{\frac{1}{3}}})$