Calculus Examples

$162.44 = \frac{11}{2} {(10)}^{2} - 8 \ln (| 10 |) + k$

Step 1

Rewrite the equation as $\frac{11}{2} \cdot 10^{2} - 8 \ln (| 10 |) + k = 162.44$ .

$\frac{11}{2} \cdot 10^{2} - 8 \ln (| 10 |) + k = 162.44$

Step 2

Simplify each term.

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Step 2.1

Raise $10$ to the power of $2$ .

$\frac{11}{2} \cdot 100 - 8 \ln (| 10 |) + k = 162.44$

Step 2.2

Cancel the common factor of $2$ .

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Step 2.2.1

Factor $2$ out of $100$ .

$\frac{11}{2} \cdot (2 (50)) - 8 \ln (| 10 |) + k = 162.44$

Step 2.2.2

Cancel the common factor.

$\frac{11}{2} \cdot (2 \cdot 50) - 8 \ln (| 10 |) + k = 162.44$

Step 2.2.3

Rewrite the expression.

$11 \cdot 50 - 8 \ln (| 10 |) + k = 162.44$

Step 2.3

Multiply $11$ by $50$ .

$550 - 8 \ln (| 10 |) + k = 162.44$

Step 2.4

The absolute value is the distance between a number and zero. The distance between $0$ and $10$ is $10$ .

$550 - 8 \ln (10) + k = 162.44$

Step 2.5

Simplify $- 8 \ln (10)$ by moving $8$ inside the logarithm.

$550 - \ln (10^{8}) + k = 162.44$

Step 2.6

Raise $10$ to the power of $8$ .

$550 - \ln (100000000) + k = 162.44$

Step 3

Move all terms not containing $k$ to the right side of the equation.

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Step 3.1

Subtract $550$ from both sides of the equation.

$- \ln (100000000) + k = 162.44 - 550$

Step 3.2

Add $\ln (100000000)$ to both sides of the equation.

$k = 162.44 - 550 + \ln (100000000)$

Step 3.3

Subtract $550$ from $162.44$ .

$k = - 387.56 + \ln (100000000)$

Step 3.4

Add $- 387.56$ and $\ln (100000000)$ .

$k = - 369.13931925$