Precalculus Examples

$y = e^{x - 2}$

Step 1

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

$e^{x - 2} = y$

Step 2

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

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

Step 3

Expand the left side.

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Step 3.1

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

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

Step 3.2

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

$(x - 2) \cdot 1 = \ln (y)$

Step 3.3

Multiply $x - 2$ by $1$ .

$x - 2 = \ln (y)$

Step 4

Add $2$ to both sides of the equation.

$x = \ln (y) + 2$