Precalculus Examples

$10 \cdot \frac{\ln (14)}{6 \ln (13) + \ln (14)}$

Step 1

Simplify the denominator.

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Step 1.1

Simplify $6 \ln (13)$ by moving $6$ inside the logarithm.

$10 \cdot \frac{\ln (14)}{\ln (13^{6}) + \ln (14)}$

Step 1.2

Raise $13$ to the power of $6$ .

$10 \cdot \frac{\ln (14)}{\ln (4826809) + \ln (14)}$

Step 1.3

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

$10 \cdot \frac{\ln (14)}{\ln (4826809 \cdot 14)}$

Step 1.4

Multiply $4826809$ by $14$ .

$10 \cdot \frac{\ln (14)}{\ln (67575326)}$

Step 2

Multiply $10 \frac{\ln (14)}{\ln (67575326)}$ .

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Step 2.1

Combine $10$ and $\frac{\ln (14)}{\ln (67575326)}$ .

$\frac{10 \ln (14)}{\ln (67575326)}$

Step 2.2

Simplify $10 \ln (14)$ by moving $10$ inside the logarithm.

$\frac{\ln (14^{10})}{\ln (67575326)}$

Step 3

Raise $14$ to the power of $10$ .

$\frac{\ln (289254654976)}{\ln (67575326)}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{\ln (289254654976)}{\ln (67575326)}$

Decimal Form:

$1.46380465 \dots$