Solve for x 8*e^(x-1)=56

$8 \cdot e^{x - 1} = 56$

Step 1

Divide each term in $(8 \cdot e^{x - 1}) = 56$ by $8$ and simplify.

Divide each term in $(8 \cdot e^{x - 1}) = 56$ by $8$ .

$\frac{(8 \cdot e^{x - 1})}{8} = \frac{56}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 \cdot e^{x - 1}}{8} = \frac{56}{8}$

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

$e^{x - 1} = \frac{56}{8}$

Simplify the right side.

Divide $56$ by $8$ .

$e^{x - 1} = 7$

Step 2

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

$\ln (e^{x - 1}) = \ln (7)$

Step 3

Expand the left side.

Expand $\ln (e^{x - 1})$ by moving $x - 1$ outside the logarithm.

$(x - 1) \ln (e) = \ln (7)$

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

$(x - 1) \cdot 1 = \ln (7)$

Multiply $x - 1$ by $1$ .

$x - 1 = \ln (7)$

Step 4

Add $1$ to both sides of the equation.

$x = \ln (7) + 1$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \ln (7) + 1$

Decimal Form:

$x = 2.94591014 \dots$