Solve for y x=2^y

$x = 2^{y}$

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

$2^{y} = x$

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

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

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

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

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

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

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

Simplify the left side.

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

Cancel the common factor.

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

Divide $y$ by $1$ .

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