Precalculus Examples

$\frac{\log (13)}{\log (6)} + 2$

Step 1

To write $2$ as a fraction with a common denominator, multiply by $\frac{\log (6)}{\log (6)}$ .

$\frac{\log (13)}{\log (6)} + \frac{2 \log (6)}{\log (6)}$

Step 2

Combine the numerators over the common denominator.

$\frac{\log (13) + 2 \log (6)}{\log (6)}$

Step 3

Simplify the numerator.

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Step 3.1

Simplify $2 \log (6)$ by moving $2$ inside the logarithm.

$\frac{\log (13) + \log (6^{2})}{\log (6)}$

Step 3.2

Raise $6$ to the power of $2$ .

$\frac{\log (13) + \log (36)}{\log (6)}$

Step 3.3

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\frac{\log (13 \cdot 36)}{\log (6)}$

Step 3.4

Multiply $13$ by $36$ .

$\frac{\log (468)}{\log (6)}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{\log (468)}{\log (6)}$

Decimal Form:

$3.43152549 \dots$