Solve for x 2e^x-1=9

$2 e^{x} - 1 = 9$

Step 1

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

Add $1$ to both sides of the equation.

$2 e^{x} = 9 + 1$

Add $9$ and $1$ .

$2 e^{x} = 10$

Step 2

Divide each term in $2 e^{x} = 10$ by $2$ and simplify.

Divide each term in $2 e^{x} = 10$ by $2$ .

$\frac{2 e^{x}}{2} = \frac{10}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 e^{x}}{2} = \frac{10}{2}$

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

$e^{x} = \frac{10}{2}$

Simplify the right side.

Divide $10$ by $2$ .

$e^{x} = 5$

Step 3

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

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

Step 4

Expand the left side.

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

$x \ln (e) = \ln (5)$

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

$x \cdot 1 = \ln (5)$

Multiply $x$ by $1$ .

$x = \ln (5)$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \ln (5)$

Decimal Form:

$x = 1.60943791 \dots$