Precalculus Examples

$\ln (2) + \ln (x) + 6 \ln (y) - \ln (z - 7)$

Step 1

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

$\ln (2 x) + 6 \ln (y) - \ln (z - 7)$

Step 2

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

$6 \ln (y) + \ln (\frac{2 x}{z - 7})$

Step 3

Simplify $6 \ln (y)$ by moving $6$ inside the logarithm.

$\ln (y^{6}) + \ln (\frac{2 x}{z - 7})$

Step 4

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

$\ln (y^{6} \frac{2 x}{z - 7})$

Step 5

Combine $y^{6}$ and $\frac{2 x}{z - 7}$ .

$\ln (\frac{y^{6} (2 x)}{z - 7})$

Step 6

Move $2$ to the left of $y^{6}$ .

$\ln (\frac{2 y^{6} x}{z - 7})$