Precalculus Examples

$\frac{\log (4) - \log (3)}{3 \log (3) - 4 \log (4)}$

Step 1

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

$\frac{\log (\frac{4}{3})}{3 \log (3) - 4 \log (4)}$

Step 2

Simplify the denominator.

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Step 2.1

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

$\frac{\log (\frac{4}{3})}{\log (3^{3}) - 4 \log (4)}$

Step 2.2

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

$\frac{\log (\frac{4}{3})}{\log (27) - 4 \log (4)}$

Step 2.3

Simplify $- 4 \log (4)$ by moving $4$ inside the logarithm.

$\frac{\log (\frac{4}{3})}{\log (27) - \log (4^{4})}$

Step 2.4

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

$\frac{\log (\frac{4}{3})}{\log (27) - \log (256)}$

Step 2.5

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

$\frac{\log (\frac{4}{3})}{\log (\frac{27}{256})}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{\log (\frac{4}{3})}{\log (\frac{27}{256})}$

Decimal Form:

$- 0.12789618 \dots$