Precalculus Examples

$\frac{\log (6144)}{\log (6)} - 1$

Step 1

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{\log (6)}{\log (6)}$ .

$\frac{\log (6144)}{\log (6)} - 1 \cdot \frac{\log (6)}{\log (6)}$

Step 2

Combine fractions.

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Step 2.1

Combine $- 1$ and $\frac{\log (6)}{\log (6)}$ .

$\frac{\log (6144)}{\log (6)} + \frac{- \log (6)}{\log (6)}$

Step 2.2

Combine the numerators over the common denominator.

$\frac{\log (6144) - \log (6)}{\log (6)}$

Step 3

Simplify the numerator.

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Step 3.1

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

$\frac{\log (\frac{6144}{6})}{\log (6)}$

Step 3.2

Divide $6144$ by $6$ .

$\frac{\log (1024)}{\log (6)}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{\log (1024)}{\log (6)}$

Decimal Form:

$3.86852807 \dots$