Finite Math Examples

$10 + 2 e^{8 x} = 30$

Step 1

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

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Step 1.1

Subtract $10$ from both sides of the equation.

$2 e^{8 x} = 30 - 10$

Step 1.2

Subtract $10$ from $30$ .

$2 e^{8 x} = 20$

Step 2

Divide each term in $2 e^{8 x} = 20$ by $2$ and simplify.

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Step 2.1

Divide each term in $2 e^{8 x} = 20$ by $2$ .

$\frac{2 e^{8 x}}{2} = \frac{20}{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{2 e^{8 x}}{2} = \frac{20}{2}$

Step 2.2.1.2

Divide $e^{8 x}$ by $1$ .

$e^{8 x} = \frac{20}{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $20$ by $2$ .

$e^{8 x} = 10$

Step 3

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

$\ln (e^{8 x}) = \ln (10)$

Step 4

Expand the left side.

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Step 4.1

Expand $\ln (e^{8 x})$ by moving $8 x$ outside the logarithm.

$8 x \ln (e) = \ln (10)$

Step 4.2

The natural logarithm of $e$ is $1$ .

$8 x \cdot 1 = \ln (10)$

Step 4.3

Multiply $8$ by $1$ .

$8 x = \ln (10)$

Step 5

Divide each term in $8 x = \ln (10)$ by $8$ and simplify.

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Step 5.1

Divide each term in $8 x = \ln (10)$ by $8$ .

$\frac{8 x}{8} = \frac{\ln (10)}{8}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $8$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{8 x}{8} = \frac{\ln (10)}{8}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{\ln (10)}{8}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (10)}{8}$

Decimal Form:

$x = 0.28782313 \dots$