Algebra Examples

$2^{x} - 1 = 0$

Step 1

Add $1$ to both sides of the equation.

$2^{x} = 1$

Step 2

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

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

Step 3

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

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

Step 4

Simplify the right side.

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Step 4.1

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

$x \ln (2) = 0$

Step 5

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

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Step 5.1

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

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

Step 5.2

Simplify the left side.

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Step 5.2.1

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

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Step 5.2.1.1

Cancel the common factor.

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

Step 5.2.1.2

Divide $x$ by $1$ .

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

Step 5.3

Simplify the right side.

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Step 5.3.1

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

$x = 0$