Solve for x 8y=3e^x

$8 y = 3 e^{x}$

Step 1

Rewrite the equation as $3 e^{x} = 8 y$ .

$3 e^{x} = 8 y$

Step 2

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

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

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

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

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

Step 3

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

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

Step 4

Expand the left side.

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

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

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

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

Multiply $x$ by $1$ .

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