Precalculus Examples

$\frac{\ln (2)}{\ln (\frac{9}{4}) + \ln (2)}$

Step 1

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

$\frac{\ln (2)}{\ln (\frac{9}{4} \cdot 2)}$

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Factor $2$ out of $4$ .

$\frac{\ln (2)}{\ln (\frac{9}{2 (2)} \cdot 2)}$

Step 2.2

Cancel the common factor.

$\frac{\ln (2)}{\ln (\frac{9}{2 \cdot 2} \cdot 2)}$

Step 2.3

Rewrite the expression.

$\frac{\ln (2)}{\ln (\frac{9}{2})}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{\ln (2)}{\ln (\frac{9}{2})}$

Decimal Form:

$0.46084542 \dots$