Precalculus Examples

$e^{\frac{\ln (10) \ln (3)}{\ln (3) + \ln (10)}}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $\ln (10)$ as $\ln (2 (5))$ .

$e^{\frac{\ln (2 (5)) \ln (3)}{\ln (3) + \ln (10)}}$

Step 1.2

Rewrite $\ln (2 (5))$ as $\ln (2) + \ln (5)$ .

$e^{\frac{(\ln (2) + \ln (5)) \ln (3)}{\ln (3) + \ln (10)}}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $\ln (10)$ as $\ln (2 (5))$ .

$e^{\frac{(\ln (2) + \ln (5)) \ln (3)}{\ln (3) + \ln (2 (5))}}$

Step 2.2

Rewrite $\ln (2 (5))$ as $\ln (2) + \ln (5)$ .

$e^{\frac{(\ln (2) + \ln (5)) \ln (3)}{\ln (3) + \ln (2) + \ln (5)}}$

Step 3

Reorder factors in $e^{\frac{(\ln (2) + \ln (5)) \ln (3)}{\ln (3) + \ln (2) + \ln (5)}}$ .

$e^{\frac{\ln (3) (\ln (2) + \ln (5))}{\ln (3) + \ln (2) + \ln (5)}}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$e^{\frac{\ln (3) (\ln (2) + \ln (5))}{\ln (3) + \ln (2) + \ln (5)}}$

Decimal Form:

$2.10381480 \dots$