Precalculus Examples

$(\frac{1}{2}) \ln (e^{4 x})$

Step 1

Use logarithm rules to move $4 x$ out of the exponent.

$\frac{1}{2} (4 x \ln (e))$

Step 2

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

$\frac{1}{2} (4 x \cdot 1)$

Step 3

Multiply $4$ by $1$ .

$\frac{1}{2} (4 x)$

Step 4

Cancel the common factor of $2$ .

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Step 4.1

Factor $2$ out of $4 x$ .

$\frac{1}{2} (2 (2 x))$

Step 4.2

Cancel the common factor.

$\frac{1}{2} (2 (2 x))$

Step 4.3

Rewrite the expression.

$2 x$