Precalculus Examples

$\frac{4 \ln (6)}{\ln (5) + \ln (6)}$

Step 1

Simplify $4 \ln (6)$ by moving $4$ inside the logarithm.

$\frac{\ln (6^{4})}{\ln (5) + \ln (6)}$

Step 2

Simplify the denominator.

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Step 2.1

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\frac{\ln (6^{4})}{\ln (5 \cdot 6)}$

Step 2.2

Multiply $5$ by $6$ .

$\frac{\ln (6^{4})}{\ln (30)}$

Step 3

Raise $6$ to the power of $4$ .

$\frac{\ln (1296)}{\ln (30)}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{\ln (1296)}{\ln (30)}$

Decimal Form:

$2.10721021 \dots$