Precalculus Examples

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

Step 1

Simplify the numerator.

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Step 1.1

Raise $3$ to the power of $2$ .

$\frac{\ln (2 \cdot 9)}{\ln ({(3 \cdot 5)}^{3})}$

Step 1.2

Multiply $2$ by $9$ .

$\frac{\ln (18)}{\ln ({(3 \cdot 5)}^{3})}$

Step 2

Simplify the denominator.

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Step 2.1

Multiply $3$ by $5$ .

$\frac{\ln (18)}{\ln (15^{3})}$

Step 2.2

Raise $15$ to the power of $3$ .

$\frac{\ln (18)}{\ln (3375)}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{\ln (18)}{\ln (3375)}$

Decimal Form:

$0.35577525 \dots$