Precalculus Examples

$\ln (3) - 2 \ln (4) + \ln (32)$

Step 1

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

$\ln (3 \cdot 32) - 2 \ln (4)$

Step 2

Simplify each term.

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Step 2.1

Multiply $3$ by $32$ .

$\ln (96) - 2 \ln (4)$

Step 2.2

Simplify $- 2 \ln (4)$ by moving $2$ inside the logarithm.

$\ln (96) - \ln (4^{2})$

Step 2.3

Raise $4$ to the power of $2$ .

$\ln (96) - \ln (16)$

Step 3

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

$\ln (\frac{96}{16})$

Step 4

Divide $96$ by $16$ .

$\ln (6)$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\ln (6)$

Decimal Form:

$1.79175946 \dots$