Precalculus Examples

$\frac{9 \ln (145) - 12}{4 - 4 \ln (145)}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $\ln (145)$ as $\ln (5 (29))$ .

$\frac{9 \ln (5 (29)) - 12}{4 - 4 \ln (145)}$

Step 1.2

Rewrite $\ln (5 (29))$ as $\ln (5) + \ln (29)$ .

$\frac{9 (\ln (5) + \ln (29)) - 12}{4 - 4 \ln (145)}$

Step 1.3

Apply the distributive property.

$\frac{9 \ln (5) + 9 \ln (29) - 12}{4 - 4 \ln (145)}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $\ln (145)$ as $\ln (5 (29))$ .

$\frac{9 \ln (5) + 9 \ln (29) - 12}{4 - 4 \ln (5 (29))}$

Step 2.2

Rewrite $\ln (5 (29))$ as $\ln (5) + \ln (29)$ .

$\frac{9 \ln (5) + 9 \ln (29) - 12}{4 - 4 (\ln (5) + \ln (29))}$

Step 2.3

Apply the distributive property.

$\frac{9 \ln (5) + 9 \ln (29) - 12}{4 - 4 \ln (5) - 4 \ln (29)}$