Precalculus Examples

$e^{x - 1} = 13$

Step 1

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

$\ln (e^{x - 1}) = \ln (13)$

Step 2

Expand the left side.

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Step 2.1

Expand $\ln (e^{x - 1})$ by moving $x - 1$ outside the logarithm.

$(x - 1) \ln (e) = \ln (13)$

Step 2.2

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

$(x - 1) \cdot 1 = \ln (13)$

Step 2.3

Multiply $x - 1$ by $1$ .

$x - 1 = \ln (13)$

Step 3

Add $1$ to both sides of the equation.

$x = \ln (13) + 1$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \ln (13) + 1$

Decimal Form:

$x = 3.56494935 \dots$