Precalculus Examples

$\frac{2 \log (5)}{\log (5) - 2 \log (3)}$

Step 1

Simplify $2 \log (5)$ by moving $2$ inside the logarithm.

$\frac{\log (5^{2})}{\log (5) - 2 \log (3)}$

Step 2

Simplify the denominator.

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Step 2.1

Simplify $- 2 \log (3)$ by moving $2$ inside the logarithm.

$\frac{\log (5^{2})}{\log (5) - \log (3^{2})}$

Step 2.2

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

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

Step 2.3

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

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

Step 3

Raise $5$ to the power of $2$ .

$\frac{\log (25)}{\log (\frac{5}{9})}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{\log (25)}{\log (\frac{5}{9})}$

Decimal Form:

$- 5.47626548 \dots$