Precalculus Examples

$10^{\frac{\frac{1}{3} \cdot \ln (36)}{\ln (10)}}$

Step 1

Simplify $\frac{1}{3} \ln (36)$ by moving $\frac{1}{3}$ inside the logarithm.

$10^{\frac{\ln (36^{\frac{1}{3}})}{\ln (10)}}$

Step 2

Use the change of base rule $\frac{\log_{b} (x)}{\log_{b} (a)} = \log_{a} (x)$ .

$10^{\log (36^{\frac{1}{3}})}$

Step 3

Exponentiation and log are inverse functions.

$36^{\frac{1}{3}}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$36^{\frac{1}{3}}$

Decimal Form:

$3.30192724 \dots$