Precalculus Examples

$8 e^{3 x} + 3 = 10$

Step 1

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

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Step 1.1

Subtract $3$ from both sides of the equation.

$8 e^{3 x} = 10 - 3$

Step 1.2

Subtract $3$ from $10$ .

$8 e^{3 x} = 7$

Step 2

Divide each term in $8 e^{3 x} = 7$ by $8$ and simplify.

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Step 2.1

Divide each term in $8 e^{3 x} = 7$ by $8$ .

$\frac{8 e^{3 x}}{8} = \frac{7}{8}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $8$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{8 e^{3 x}}{8} = \frac{7}{8}$

Step 2.2.1.2

Divide $e^{3 x}$ by $1$ .

$e^{3 x} = \frac{7}{8}$

Step 3

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

$\ln (e^{3 x}) = \ln (\frac{7}{8})$

Step 4

Expand the left side.

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Step 4.1

Expand $\ln (e^{3 x})$ by moving $3 x$ outside the logarithm.

$3 x \ln (e) = \ln (\frac{7}{8})$

Step 4.2

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

$3 x \cdot 1 = \ln (\frac{7}{8})$

Step 4.3

Multiply $3$ by $1$ .

$3 x = \ln (\frac{7}{8})$

Step 5

Divide each term in $3 x = \ln (\frac{7}{8})$ by $3$ and simplify.

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Step 5.1

Divide each term in $3 x = \ln (\frac{7}{8})$ by $3$ .

$\frac{3 x}{3} = \frac{\ln (\frac{7}{8})}{3}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $3$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{\ln (\frac{7}{8})}{3}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{\ln (\frac{7}{8})}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (\frac{7}{8})}{3}$

Decimal Form:

$x = - 0.04451046 \dots$