Precalculus Examples

$e^{x} - 9 = 19$

Step 1

Move all terms not containing $x$ to the right side of the equation.

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Step 1.1

Add $9$ to both sides of the equation.

$e^{x} = 19 + 9$

Step 1.2

Add $19$ and $9$ .

$e^{x} = 28$

Step 2

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

$\ln (e^{x}) = \ln (28)$

Step 3

Expand the left side.

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Step 3.1

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

$x \ln (e) = \ln (28)$

Step 3.2

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

$x \cdot 1 = \ln (28)$

Step 3.3

Multiply $x$ by $1$ .

$x = \ln (28)$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \ln (28)$

Decimal Form:

$x = 3.33220451 \dots$