Precalculus Examples

$4 \ln (2) + 0.5 \ln (9) - \ln (6)$

Step 1

Simplify each term.

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Step 1.1

Rewrite $\ln (9)$ as $\ln (3^{2})$ .

$4 \ln (2) + 0.5 \ln (3^{2}) - \ln (6)$

Step 1.2

Expand $\ln (3^{2})$ by moving $2$ outside the logarithm.

$4 \ln (2) + 0.5 (2 \ln (3)) - \ln (6)$

Step 1.3

Multiply $0.5 (2 \ln (3))$ .

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Step 1.3.1

Multiply $2$ by $0.5$ .

$4 \ln (2) + 1 \ln (3) - \ln (6)$

Step 1.3.2

Multiply $\ln (3)$ by $1$ .

$4 \ln (2) + \ln (3) - \ln (6)$

$4 \ln (2) + \ln (3) - \ln (6)$

Step 1.4

Rewrite $\ln (6)$ as $\ln (2 (3))$ .

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

Step 1.5

Rewrite $\ln (2 (3))$ as $\ln (2) + \ln (3)$ .

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

Step 1.6

Apply the distributive property.

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

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

Step 2

Subtract $\ln (3)$ from $\ln (3)$ .

$4 \ln (2) + 0 - \ln (2)$

Step 3

Add $4 \ln (2)$ and $0$ .

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

Step 4

Subtract $\ln (2)$ from $4 \ln (2)$ .

$3 \ln (2)$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$