Precalculus Examples

$e^{\frac{\ln (8) \ln (7)}{\ln (7) + \ln (8)}}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $\ln (8)$ as $\ln (2^{3})$ .

$e^{\frac{\ln (2^{3}) \ln (7)}{\ln (7) + \ln (8)}}$

Step 1.2

Expand $\ln (2^{3})$ by moving $3$ outside the logarithm.

$e^{\frac{3 \ln (2) \ln (7)}{\ln (7) + \ln (8)}}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $\ln (8)$ as $\ln (2^{3})$ .

$e^{\frac{3 \ln (2) \ln (7)}{\ln (7) + \ln (2^{3})}}$

Step 2.2

Expand $\ln (2^{3})$ by moving $3$ outside the logarithm.

$e^{\frac{3 \ln (2) \ln (7)}{\ln (7) + 3 \ln (2)}}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$e^{\frac{3 \ln (2) \ln (7)}{\ln (7) + 3 \ln (2)}}$

Decimal Form:

$2.73253712 \dots$