Precalculus Examples

$2 \ln (3 x - 1) + \ln (5) - \ln (x)$

Step 1

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

$2 \ln (3 x - 1) + \ln (\frac{5}{x})$

Step 2

Simplify $2 \ln (3 x - 1)$ by moving $2$ inside the logarithm.

$\ln ({(3 x - 1)}^{2}) + \ln (\frac{5}{x})$

Step 3

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

$\ln ({(3 x - 1)}^{2} \frac{5}{x})$

Step 4

Combine ${(3 x - 1)}^{2}$ and $\frac{5}{x}$ .

$\ln (\frac{{(3 x - 1)}^{2} \cdot 5}{x})$

Step 5

Move $5$ to the left of ${(3 x - 1)}^{2}$ .

$\ln (\frac{5 {(3 x - 1)}^{2}}{x})$