Precalculus Examples

$\frac{2 \log (9)}{\log (\frac{6}{5}) + 2 \log (9)}$

Step 1

Simplify $2 \log (9)$ by moving $2$ inside the logarithm.

$\frac{\log (9^{2})}{\log (\frac{6}{5}) + 2 \log (9)}$

Step 2

Simplify the denominator.

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Step 2.1

Simplify $2 \log (9)$ by moving $2$ inside the logarithm.

$\frac{\log (9^{2})}{\log (\frac{6}{5}) + \log (9^{2})}$

Step 2.2

Raise $9$ to the power of $2$ .

$\frac{\log (9^{2})}{\log (\frac{6}{5}) + \log (81)}$

Step 2.3

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

$\frac{\log (9^{2})}{\log (\frac{6}{5} \cdot 81)}$

Step 2.4

Multiply $\frac{6}{5} \cdot 81$ .

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Step 2.4.1

Combine $\frac{6}{5}$ and $81$ .

$\frac{\log (9^{2})}{\log (\frac{6 \cdot 81}{5})}$

Step 2.4.2

Multiply $6$ by $81$ .

$\frac{\log (9^{2})}{\log (\frac{486}{5})}$

Step 3

Raise $9$ to the power of $2$ .

$\frac{\log (81)}{\log (\frac{486}{5})}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{\log (81)}{\log (\frac{486}{5})}$

Decimal Form:

$0.96016371 \dots$