Precalculus Examples

$\ln (3) + \frac{1}{3} \cdot \ln (4 - x^{2}) - \ln (x)$

Step 1

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

$\frac{1}{3} \cdot \ln (4 - x^{2}) + \ln (\frac{3}{x})$

Step 2

Simplify $\frac{1}{3} \ln (4 - x^{2})$ by moving $\frac{1}{3}$ inside the logarithm.

$\ln ({(4 - x^{2})}^{\frac{1}{3}}) + \ln (\frac{3}{x})$

Step 3

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

$\ln ({(4 - x^{2})}^{\frac{1}{3}} \frac{3}{x})$

Step 4

Combine ${(4 - x^{2})}^{\frac{1}{3}}$ and $\frac{3}{x}$ .

$\ln (\frac{{(4 - x^{2})}^{\frac{1}{3}} \cdot 3}{x})$

Step 5

Move $3$ to the left of ${(4 - x^{2})}^{\frac{1}{3}}$ .

$\ln (\frac{3 {(4 - x^{2})}^{\frac{1}{3}}}{x})$