Calculus Examples

$x^{y} = y^{x}$

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

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

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