Precalculus Examples

$\frac{- 13 + 4 \ln (90)}{1 + 5 \ln (90)}$

Step 1

Simplify the numerator.

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Step 1.1

Simplify $4 \ln (90)$ by moving $4$ inside the logarithm.

$\frac{- 13 + \ln (90^{4})}{1 + 5 \ln (90)}$

Step 1.2

Raise $90$ to the power of $4$ .

$\frac{- 13 + \ln (65610000)}{1 + 5 \ln (90)}$

Step 2

Simplify the denominator.

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Step 2.1

Simplify $5 \ln (90)$ by moving $5$ inside the logarithm.

$\frac{- 13 + \ln (65610000)}{1 + \ln (90^{5})}$

Step 2.2

Raise $90$ to the power of $5$ .

$\frac{- 13 + \ln (65610000)}{1 + \ln (5904900000)}$

Step 3

Simplify with factoring out.

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Step 3.1

Rewrite $- 13$ as $- 1 (13)$ .

$\frac{- 1 (13) + \ln (65610000)}{1 + \ln (5904900000)}$

Step 3.2

Factor $- 1$ out of $\ln (65610000)$ .

$\frac{- 1 (13) - 1 (- \ln (65610000))}{1 + \ln (5904900000)}$

Step 3.3

Factor $- 1$ out of $- 1 (13) - 1 (- \ln (65610000))$ .

$\frac{- 1 (13 - \ln (65610000))}{1 + \ln (5904900000)}$

Step 3.4

Move the negative in front of the fraction.

$- \frac{13 - \ln (65610000)}{1 + \ln (5904900000)}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \frac{13 - \ln (65610000)}{1 + \ln (5904900000)}$

Decimal Form:

$0.21274217 \dots$