Solve for x 4e^x=10

$4 e^{x} = 10$

Step 1

Divide each term in $4 e^{x} = 10$ by $4$ and simplify.

Divide each term in $4 e^{x} = 10$ by $4$ .

$\frac{4 e^{x}}{4} = \frac{10}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 e^{x}}{4} = \frac{10}{4}$

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

$e^{x} = \frac{10}{4}$

Simplify the right side.

Cancel the common factor of $10$ and $4$ .

Factor $2$ out of $10$ .

$e^{x} = \frac{2 (5)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$e^{x} = \frac{2 \cdot 5}{2 \cdot 2}$

Cancel the common factor.

$e^{x} = \frac{2 \cdot 5}{2 \cdot 2}$

Rewrite the expression.

$e^{x} = \frac{5}{2}$

Step 2

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

$\ln (e^{x}) = \ln (\frac{5}{2})$

Step 3

Expand the left side.

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

$x \ln (e) = \ln (\frac{5}{2})$

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

$x \cdot 1 = \ln (\frac{5}{2})$

Multiply $x$ by $1$ .

$x = \ln (\frac{5}{2})$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \ln (\frac{5}{2})$

Decimal Form:

$x = 0.91629073 \dots$