Solve for x y=e+2^x

$y = e + 2^{x}$

Step 1

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

$e + 2^{x} = y$

Step 2

Subtract $e$ from both sides of the equation.

$2^{x} = y - e$

Step 3

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

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

Step 4

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

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

Step 5

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

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

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

Simplify the left side.

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

Cancel the common factor.

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

Divide $x$ by $1$ .

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