Precalculus Examples

$- \frac{4 \ln (15)}{3 \ln (11) - \ln (15)}$

Step 1

Simplify $4 \ln (15)$ by moving $4$ inside the logarithm.

$- \frac{\ln (15^{4})}{3 \ln (11) - \ln (15)}$

Step 2

Simplify the denominator.

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Step 2.1

Simplify $3 \ln (11)$ by moving $3$ inside the logarithm.

$- \frac{\ln (15^{4})}{\ln (11^{3}) - \ln (15)}$

Step 2.2

Raise $11$ to the power of $3$ .

$- \frac{\ln (15^{4})}{\ln (1331) - \ln (15)}$

Step 2.3

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

$- \frac{\ln (15^{4})}{\ln (\frac{1331}{15})}$

Step 3

Raise $15$ to the power of $4$ .

$- \frac{\ln (50625)}{\ln (\frac{1331}{15})}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \frac{\ln (50625)}{\ln (\frac{1331}{15})}$

Decimal Form:

$- 2.41486418 \dots$