Precalculus Examples

$e^{x} + 5 = 60$

Step 1

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

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Step 1.1

Subtract $5$ from both sides of the equation.

$e^{x} = 60 - 5$

Step 1.2

Subtract $5$ from $60$ .

$e^{x} = 55$

Step 2

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

$\ln (e^{x}) = \ln (55)$

Step 3

Expand the left side.

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Step 3.1

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

$x \ln (e) = \ln (55)$

Step 3.2

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

$x \cdot 1 = \ln (55)$

Step 3.3

Multiply $x$ by $1$ .

$x = \ln (55)$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \ln (55)$

Decimal Form:

$x = 4.00733318 \dots$