Write as a Single Logarithm 3 natural log of 3- natural log of 9

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

Step 1

Simplify each term.

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

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

Raise $3$ to the power of $3$ .

$\ln (27) - \ln (9)$

Step 2

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

$\ln (\frac{27}{9})$

Step 3

Divide $27$ by $9$ .

$\ln (3)$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\ln (3)$

Decimal Form:

$1.09861228 \dots$