Precalculus Examples

$\frac{\ln (28)}{\ln (2)} + 2$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $\ln (28)$ as $\ln (2^{2} \cdot 7)$ .

$\frac{\ln (2^{2} \cdot 7)}{\ln (2)} + 2$

Step 1.2

Rewrite $\ln (2^{2} \cdot 7)$ as $\ln (2^{2}) + \ln (7)$ .

$\frac{\ln (2^{2}) + \ln (7)}{\ln (2)} + 2$

Step 1.3

Expand $\ln (2^{2})$ by moving $2$ outside the logarithm.

$\frac{2 \ln (2) + \ln (7)}{\ln (2)} + 2$

Step 2

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

$\frac{2 \ln (2) + \ln (7)}{\ln (2)} + \frac{2 \ln (2)}{\ln (2)}$

Step 3

Combine the numerators over the common denominator.

$\frac{2 \ln (2) + \ln (7) + 2 \ln (2)}{\ln (2)}$

Step 4

Add $2 \ln (2)$ and $2 \ln (2)$ .

$\frac{4 \ln (2) + \ln (7)}{\ln (2)}$