Solve for x y=2^x

$y = 2^{x}$

Step 1

Rewrite the equation as $2^{x} = y$ .

$2^{x} = y$

Step 2

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

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

Step 3

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

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

Step 4

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

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

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

Simplify the left side.

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

Cancel the common factor.

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

Divide $x$ by $1$ .

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