Precalculus Examples

$\frac{2 (\log (3 y^{- 1}))}{3}$

Step 1

Rewrite $\frac{2 (\log (3 y^{- 1}))}{3}$ as $\frac{2}{3} \log (3 y^{- 1})$ .

$\frac{2}{3} \log (3 y^{- 1})$

Step 2

Simplify $\frac{2}{3} \log (3 y^{- 1})$ by moving $\frac{2}{3}$ inside the logarithm.

$\log ({(3 y^{- 1})}^{\frac{2}{3}})$

Step 3

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\log ({(3 \frac{1}{y})}^{\frac{2}{3}})$

Step 4

Combine $3$ and $\frac{1}{y}$ .

$\log ({(\frac{3}{y})}^{\frac{2}{3}})$

Step 5

Apply the product rule to $\frac{3}{y}$ .

$\log (\frac{3^{\frac{2}{3}}}{y^{\frac{2}{3}}})$