Precalculus Examples

$\frac{9 \ln (8)}{\ln (8) + 10 \ln (3)}$

Step 1

Simplify $9 \ln (8)$ by moving $9$ inside the logarithm.

$\frac{\ln (8^{9})}{\ln (8) + 10 \ln (3)}$

Step 2

Simplify the denominator.

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Step 2.1

Simplify $10 \ln (3)$ by moving $10$ inside the logarithm.

$\frac{\ln (8^{9})}{\ln (8) + \ln (3^{10})}$

Step 2.2

Raise $3$ to the power of $10$ .

$\frac{\ln (8^{9})}{\ln (8) + \ln (59049)}$

Step 2.3

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

$\frac{\ln (8^{9})}{\ln (8 \cdot 59049)}$

Step 2.4

Multiply $8$ by $59049$ .

$\frac{\ln (8^{9})}{\ln (472392)}$

Step 3

Raise $8$ to the power of $9$ .

$\frac{\ln (134217728)}{\ln (472392)}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{\ln (134217728)}{\ln (472392)}$

Decimal Form:

$1.43238923 \dots$