Precalculus Examples

$\ln (4 e^{3 x})$

Step 1

Rewrite $\ln (4 e^{3 x})$ as $\ln (4) + \ln (e^{3 x})$ .

$\ln (4) + \ln (e^{3 x})$

Step 2

Use logarithm rules to move $3 x$ out of the exponent.

$\ln (4) + 3 x \ln (e)$

Step 3

The natural logarithm of $e$ is $1$ .

$\ln (4) + 3 x \cdot 1$

Step 4

Multiply $3$ by $1$ .

$\ln (4) + 3 x$

Step 5

Simplify each term.

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Step 5.1

Rewrite $\ln (4)$ as $\ln (2^{2})$ .

$\ln (2^{2}) + 3 x$

Step 5.2

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

$2 \ln (2) + 3 x$

Step 6

Reorder $2 \ln (2)$ and $3 x$ .

$3 x + 2 \ln (2)$