Precalculus Examples

$\ln (8) + 4 \ln (x) - \ln (3)$

Step 1

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

$4 \ln (x) + \ln (\frac{8}{3})$

Step 2

Simplify $4 \ln (x)$ by moving $4$ inside the logarithm.

$\ln (x^{4}) + \ln (\frac{8}{3})$

Step 3

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

$\ln (x^{4} \frac{8}{3})$

Step 4

Combine $x^{4}$ and $\frac{8}{3}$ .

$\ln (\frac{x^{4} \cdot 8}{3})$

Step 5

Move $8$ to the left of $x^{4}$ .

$\ln (\frac{8 x^{4}}{3})$