Precalculus Examples

$3^{- \frac{2 (\ln (10))}{\ln (3)}}$

Step 1

Simplify $2 \ln (10)$ by moving $2$ inside the logarithm.

$3^{- \frac{\ln (10^{2})}{\ln (3)}}$

Step 2

Raise $10$ to the power of $2$ .

$3^{- \frac{\ln (100)}{\ln (3)}}$

Step 3

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

$3^{- \log_{3} (100)}$

Step 4

Simplify $- \log_{3} (100)$ by moving $- 1$ inside the logarithm.

$3^{\log_{3} (100^{- 1})}$

Step 5

Exponentiation and log are inverse functions.

$100^{- 1}$

Step 6

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{100}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{100}$

Decimal Form:

$0.01$