Precalculus Examples

$\frac{1}{5} \ln (x) + \frac{2}{5} \ln (z) - 2 \ln (y)$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Simplify $\frac{1}{5} \ln (x)$ by moving $\frac{1}{5}$ inside the logarithm.

$\ln (x^{\frac{1}{5}}) + \frac{2}{5} \cdot \ln (z) - 2 \ln (y)$

Step 1.2

Simplify $\frac{2}{5} \ln (z)$ by moving $\frac{2}{5}$ inside the logarithm.

$\ln (x^{\frac{1}{5}}) + \ln (z^{\frac{2}{5}}) - 2 \ln (y)$

Step 1.3

Simplify $- 2 \ln (y)$ by moving $2$ inside the logarithm.

$\ln (x^{\frac{1}{5}}) + \ln (z^{\frac{2}{5}}) - \ln (y^{2})$

Step 2

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

$\ln (x^{\frac{1}{5}} z^{\frac{2}{5}}) - \ln (y^{2})$

Step 3

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

$\ln (\frac{x^{\frac{1}{5}} z^{\frac{2}{5}}}{y^{2}})$