Precalculus Examples

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

Step 1

Simplify $- \ln (\frac{3}{2})$ by moving $- 1$ inside the logarithm.

$e^{\ln ({(\frac{3}{2})}^{- 1})}$

Step 2

Exponentiation and log are inverse functions.

${(\frac{3}{2})}^{- 1}$

Step 3

Change the sign of the exponent by rewriting the base as its reciprocal.

$\frac{2}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{3}$

Decimal Form:

$0.\overline{6}$