Precalculus Examples

$\frac{\frac{\ln (87)}{\ln (9)} + 1}{2}$

Step 1

Simplify the numerator.

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Step 1.1

Write $1$ as a fraction with a common denominator.

$\frac{\frac{\ln (87)}{\ln (9)} + \frac{\ln (9)}{\ln (9)}}{2}$

Step 1.2

Combine the numerators over the common denominator.

$\frac{\frac{\ln (87) + \ln (9)}{\ln (9)}}{2}$

Step 1.3

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

$\frac{\frac{\ln (87 \cdot 9)}{\ln (9)}}{2}$

Step 1.4

Multiply $87$ by $9$ .

$\frac{\frac{\ln (783)}{\ln (9)}}{2}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{\ln (783)}{\ln (9)} \cdot \frac{1}{2}$

Step 3

Multiply $\frac{\ln (783)}{\ln (9)} \cdot \frac{1}{2}$ .

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Step 3.1

Multiply $\frac{\ln (783)}{\ln (9)}$ by $\frac{1}{2}$ .

$\frac{\ln (783)}{\ln (9) \cdot 2}$

Step 3.2

Reorder $\ln (9)$ and $2$ .

$\frac{\ln (783)}{2 \cdot \ln (9)}$

Step 3.3

Simplify $2 \cdot \ln (9)$ by moving $2$ inside the logarithm.

$\frac{\ln (783)}{\ln (9^{2})}$

Step 4

Raise $9$ to the power of $2$ .

$\frac{\ln (783)}{\ln (81)}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{\ln (783)}{\ln (81)}$

Decimal Form:

$1.51626118 \dots$