Precalculus Examples

$\frac{2 \ln (e^{r})}{e^{\ln (\frac{1}{p})}}$

Step 1

Simplify the numerator.

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Step 1.1

Use logarithm rules to move $r$ out of the exponent.

$\frac{2 (r \ln (e))}{e^{\ln (\frac{1}{p})}}$

Step 1.2

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

$\frac{2 (r \cdot 1)}{e^{\ln (\frac{1}{p})}}$

Step 1.3

Multiply $r$ by $1$ .

$\frac{2 r}{e^{\ln (\frac{1}{p})}}$

Step 2

Exponentiation and log are inverse functions.

$\frac{2 r}{\frac{1}{p}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$2 r p$