Precalculus Examples

$3 (\ln (3 - \ln (x))) + (\ln (x) - \ln (9))$

Step 1

Remove parentheses.

$3 (\ln (3 - \ln (x))) + \ln (x) - \ln (9)$

Step 2

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

$3 (\ln (3 - \ln (x))) + \ln (\frac{x}{9})$

Step 3

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

$\ln ({(3 - \ln (x))}^{3}) + \ln (\frac{x}{9})$

Step 4

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

$\ln ({(3 - \ln (x))}^{3} \frac{x}{9})$

Step 5

Combine ${(3 - \ln (x))}^{3}$ and $\frac{x}{9}$ .

$\ln (\frac{{(3 - \ln (x))}^{3} x}{9})$

Step 6

Reorder factors in $\ln (\frac{{(3 - \ln (x))}^{3} x}{9})$ .

$\ln (\frac{x {(3 - \ln (x))}^{3}}{9})$