Precalculus Examples

$\frac{0.361 (- 1) + 1.9}{{(0.19 (- 1) + 1)}^{3}} - \frac{1.9 \ln (0.19 (- 1) + 1)}{{(0.19 (- 1) + 1)}^{2}}$

Step 1

Simplify the expression.

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Step 1.1

Multiply $0.361$ by $- 1$ .

$\frac{- 0.361 + 1.9}{{(0.19 (- 1) + 1)}^{3}} - \frac{1.9 \ln (0.19 (- 1) + 1)}{{(0.19 (- 1) + 1)}^{2}}$

Step 1.2

Add $- 0.361$ and $1.9$ .

$\frac{1.539}{{(0.19 (- 1) + 1)}^{3}} - \frac{1.9 \ln (0.19 (- 1) + 1)}{{(0.19 (- 1) + 1)}^{2}}$

Step 2

Simplify each term.

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Step 2.1

Simplify the denominator.

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Step 2.1.1

Multiply $0.19$ by $- 1$ .

$\frac{1.539}{{(- 0.19 + 1)}^{3}} - \frac{1.9 \ln (0.19 (- 1) + 1)}{{(0.19 (- 1) + 1)}^{2}}$

Step 2.1.2

Add $- 0.19$ and $1$ .

$\frac{1.539}{{0.81}^{3}} - \frac{1.9 \ln (0.19 (- 1) + 1)}{{(0.19 (- 1) + 1)}^{2}}$

Step 2.1.3

Raise $0.81$ to the power of $3$ .

$\frac{1.539}{0.531441} - \frac{1.9 \ln (0.19 (- 1) + 1)}{{(0.19 (- 1) + 1)}^{2}}$

Step 2.2

Divide $1.539$ by $0.531441$ .

$2.89590001 - \frac{1.9 \ln (0.19 (- 1) + 1)}{{(0.19 (- 1) + 1)}^{2}}$

Step 2.3

Simplify $1.9 \ln (0.19 (- 1) + 1)$ by moving $1.9$ inside the logarithm.

$2.89590001 - \frac{\ln ({(0.19 (- 1) + 1)}^{1.9})}{{(0.19 (- 1) + 1)}^{2}}$

Step 2.4

Simplify the denominator.

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Step 2.4.1

Multiply $0.19$ by $- 1$ .

$2.89590001 - \frac{\ln ({(0.19 (- 1) + 1)}^{1.9})}{{(- 0.19 + 1)}^{2}}$

Step 2.4.2

Add $- 0.19$ and $1$ .

$2.89590001 - \frac{\ln ({(0.19 (- 1) + 1)}^{1.9})}{{0.81}^{2}}$

Step 2.4.3

Raise $0.81$ to the power of $2$ .

$2.89590001 - \frac{\ln ({(0.19 (- 1) + 1)}^{1.9})}{0.6561}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $0.19$ by $- 1$ .

$2.89590001 - \frac{\ln ({(- 0.19 + 1)}^{1.9})}{0.6561}$

Step 2.5.2

Add $- 0.19$ and $1$ .

$2.89590001 - \frac{\ln ({0.81}^{1.9})}{0.6561}$

Step 2.5.3

Raise $0.81$ to the power of $1.9$ .

$2.89590001 - \frac{\ln (0.6700721)}{0.6561}$

Step 2.6

Replace $e$ with an approximation.

$2.89590001 - \frac{\log_{2.71828182} (0.6700721)}{0.6561}$

Step 2.7

Log base $2.71828182$ of $0.6700721$ is approximately $- 0.40036995$ .

$2.89590001 - \frac{- 0.40036995}{0.6561}$

Step 2.8

Divide $- 0.40036995$ by $0.6561$ .

$2.89590001 - - 0.61022703$

Step 2.9

Multiply $- 1$ by $- 0.61022703$ .

$2.89590001 + 0.61022703$

Step 3

Add $2.89590001$ and $0.61022703$ .

$3.50612705$