Simplify/Condense 2 natural log of 7-3 natural log of 4

$2 \ln (7) - 3 \ln (4)$

Simplify each term.

Simplify $2 \ln (7)$ by moving $2$ inside the logarithm.

$\ln (7^{2}) - 3 \ln (4)$

Raise $7$ to the power of $2$ .

$\ln (49) - 3 \ln (4)$

Simplify $- 3 \ln (4)$ by moving $3$ inside the logarithm.

$\ln (49) - \ln (4^{3})$

Raise $4$ to the power of $3$ .

$\ln (49) - \ln (64)$

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

$\ln (\frac{49}{64})$

The result can be shown in multiple forms.

Exact Form:

$\ln (\frac{49}{64})$

Decimal Form:

$- 0.26706278 \dots$