Finite Math Examples

$R (162) = 0.37 \cdot \ln (162) + 0.05$

Step 1

Move all the expressions to the left side of the equation.

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Step 1.1

Subtract $0.37 \cdot \ln (162)$ from both sides of the equation.

$R (162) - 0.37 \cdot \ln (162) = 0.05$

Step 1.2

Subtract $0.05$ from both sides of the equation.

$R (162) - 0.37 \cdot \ln (162) - 0.05 = 0$

Step 2

Simplify $R (162) - 0.37 \cdot \ln (162) - 0.05$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Move $162$ to the left of $R$ .

$162 R - 0.37 \cdot \ln (162) - 0.05 = 0$

Step 2.1.2

Simplify $- 0.37 \ln (162)$ by moving $0.37$ inside the logarithm.

$162 R - \ln (162^{0.37}) - 0.05 = 0$

Step 2.1.3

Raise $162$ to the power of $0.37$ .

$162 R - \ln (6.56932208) - 0.05 = 0$

Step 2.2

Subtract $0.05$ from $- \ln (6.56932208)$ .

$162 R - 1.93241064 = 0$

Step 3

Add $1.93241064$ to both sides of the equation.

$162 R = 1.93241064$

Step 4

Divide each term in $162 R = 1.93241064$ by $162$ and simplify.

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Step 4.1

Divide each term in $162 R = 1.93241064$ by $162$ .

$\frac{162 R}{162} = \frac{1.93241064}{162}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $162$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{162 R}{162} = \frac{1.93241064}{162}$

Step 4.2.1.2

Divide $R$ by $1$ .

$R = \frac{1.93241064}{162}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $1.93241064$ by $162$ .

$R = 0.01192846$