Precalculus Examples

$\frac{6 \ln (2)}{\ln (2) + 4 \ln (3)}$

Step 1

Simplify $6 \ln (2)$ by moving $6$ inside the logarithm.

$\frac{\ln (2^{6})}{\ln (2) + 4 \ln (3)}$

Step 2

Simplify the denominator.

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Step 2.1

Simplify $4 \ln (3)$ by moving $4$ inside the logarithm.

$\frac{\ln (2^{6})}{\ln (2) + \ln (3^{4})}$

Step 2.2

Raise $3$ to the power of $4$ .

$\frac{\ln (2^{6})}{\ln (2) + \ln (81)}$

Step 2.3

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

$\frac{\ln (2^{6})}{\ln (2 \cdot 81)}$

Step 2.4

Multiply $2$ by $81$ .

$\frac{\ln (2^{6})}{\ln (162)}$

Step 3

Raise $2$ to the power of $6$ .

$\frac{\ln (64)}{\ln (162)}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{\ln (64)}{\ln (162)}$

Decimal Form:

$0.81745539 \dots$