Solve for x 2^x-1=0

$2^{x} - 1 = 0$

Add $1$ to both sides of the equation.

$2^{x} = 1$

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

$\ln (2^{x}) = \ln (1)$

Expand $\ln (2^{x})$ by moving $x$ outside the logarithm.

$x \ln (2) = \ln (1)$

Simplify the right side.

The natural logarithm of $1$ is $0$ .

$x \ln (2) = 0$

Divide each term in $x \ln (2) = 0$ by $\ln (2)$ and simplify.

Divide each term in $x \ln (2) = 0$ by $\ln (2)$ .

$\frac{x \ln (2)}{\ln (2)} = \frac{0}{\ln (2)}$

Simplify the left side.

Cancel the common factor of $\ln (2)$ .

Cancel the common factor.

$\frac{x \ln (2)}{\ln (2)} = \frac{0}{\ln (2)}$

Divide $x$ by $1$ .

$x = \frac{0}{\ln (2)}$

Simplify the right side.

Divide $0$ by $\ln (2)$ .

$x = 0$