Calculus Examples

$x = e^{y}$

Step 1

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

$e^{y} = x$

Step 2

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

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

Step 3

Expand the left side.

Tap for more steps...

Step 3.1

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

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

Step 3.2

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

$y \cdot 1 = \ln (x)$

Step 3.3

Multiply $y$ by $1$ .

$y = \ln (x)$