Evaluate 8e^(4x+8)=15

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

Step 1

Divide each term in $8 e^{4 x + 8} = 15$ by $8$ and simplify.

Divide each term in $8 e^{4 x + 8} = 15$ by $8$ .

$\frac{8 e^{4 x + 8}}{8} = \frac{15}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 e^{4 x + 8}}{8} = \frac{15}{8}$

Divide $e^{4 x + 8}$ by $1$ .

$e^{4 x + 8} = \frac{15}{8}$

Step 2

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

$\ln (e^{4 x + 8}) = \ln (\frac{15}{8})$

Step 3

Expand the left side.

Expand $\ln (e^{4 x + 8})$ by moving $4 x + 8$ outside the logarithm.

$(4 x + 8) \ln (e) = \ln (\frac{15}{8})$

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

$(4 x + 8) \cdot 1 = \ln (\frac{15}{8})$

Multiply $4 x + 8$ by $1$ .

$4 x + 8 = \ln (\frac{15}{8})$

Step 4

Subtract $8$ from both sides of the equation.

$4 x = \ln (\frac{15}{8}) - 8$

Step 5

Divide each term in $4 x = \ln (\frac{15}{8}) - 8$ by $4$ and simplify.

Divide each term in $4 x = \ln (\frac{15}{8}) - 8$ by $4$ .

$\frac{4 x}{4} = \frac{\ln (\frac{15}{8})}{4} + \frac{- 8}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{\ln (\frac{15}{8})}{4} + \frac{- 8}{4}$

Divide $x$ by $1$ .

$x = \frac{\ln (\frac{15}{8})}{4} + \frac{- 8}{4}$

Simplify the right side.

Divide $- 8$ by $4$ .

$x = \frac{\ln (\frac{15}{8})}{4} - 2$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (\frac{15}{8})}{4} - 2$

Decimal Form:

$x = - 1.84284783 \dots$