Solve for x 8e^(3x)+4=15

$8 e^{3 x} + 4 = 15$

Step 1

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

Subtract $4$ from both sides of the equation.

$8 e^{3 x} = 15 - 4$

Subtract $4$ from $15$ .

$8 e^{3 x} = 11$

Step 2

Divide each term in $8 e^{3 x} = 11$ by $8$ and simplify.

Divide each term in $8 e^{3 x} = 11$ by $8$ .

$\frac{8 e^{3 x}}{8} = \frac{11}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 e^{3 x}}{8} = \frac{11}{8}$

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

$e^{3 x} = \frac{11}{8}$

Step 3

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

$\ln (e^{3 x}) = \ln (\frac{11}{8})$

Step 4

Expand the left side.

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

$3 x \ln (e) = \ln (\frac{11}{8})$

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

$3 x \cdot 1 = \ln (\frac{11}{8})$

Multiply $3$ by $1$ .

$3 x = \ln (\frac{11}{8})$

Step 5

Divide each term in $3 x = \ln (\frac{11}{8})$ by $3$ and simplify.

Divide each term in $3 x = \ln (\frac{11}{8})$ by $3$ .

$\frac{3 x}{3} = \frac{\ln (\frac{11}{8})}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{\ln (\frac{11}{8})}{3}$

Divide $x$ by $1$ .

$x = \frac{\ln (\frac{11}{8})}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (\frac{11}{8})}{3}$

Decimal Form:

$x = 0.10615124 \dots$