Precalculus Examples

$\frac{\log_{6} (15)}{\log_{6} (6)}$

Step 1

Logarithm base $6$ of $6$ is $1$ .

$\frac{\log_{6} (15)}{1}$

Step 2

Divide $\log_{6} (15)$ by $1$ .

$\log_{6} (15)$

Step 3

Rewrite $\log_{6} (15)$ using the change of base formula.

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Step 3.1

The change of base rule can be used if $a$ and $b$ are greater than $0$ and not equal to $1$ , and $x$ is greater than $0$ .

$\log_{a} (x) = \frac{\log_{b} (x)}{\log_{b} (a)}$

Step 3.2

Substitute in values for the variables in the change of base formula, using $b = 10$ .

$\frac{\log (15)}{\log (6)}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{\log (15)}{\log (6)}$

Decimal Form:

$1.51139159 \dots$