Precalculus Examples

$\frac{\ln (6 + 2) \ln (5)}{3 \ln (5) - \ln (6)}$

Step 1

Simplify the numerator.

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Step 1.1

Add $6$ and $2$ .

$\frac{\ln (8) \ln (5)}{3 \ln (5) - \ln (6)}$

Step 1.2

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

$\frac{\ln (2^{3}) \ln (5)}{3 \ln (5) - \ln (6)}$

Step 1.3

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

$\frac{3 \ln (2) \ln (5)}{3 \ln (5) - \ln (6)}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $\ln (6)$ as $\ln (2 (3))$ .

$\frac{3 \ln (2) \ln (5)}{3 \ln (5) - \ln (2 (3))}$

Step 2.2

Rewrite $\ln (2 (3))$ as $\ln (2) + \ln (3)$ .

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

Step 2.3

Apply the distributive property.

$\frac{3 \ln (2) \ln (5)}{3 \ln (5) - \ln (2) - \ln (3)}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{3 \ln (2) \ln (5)}{3 \ln (5) - \ln (2) - \ln (3)}$

Decimal Form:

$1.10214794 \dots$