Precalculus Examples

$2 e^{x} + e^{x} - 15 = 0$

Step 1

Add $2 e^{x}$ and $e^{x}$ .

$3 e^{x} - 15 = 0$

Step 2

Add $15$ to both sides of the equation.

$3 e^{x} = 15$

Step 3

Divide each term in $3 e^{x} = 15$ by $3$ and simplify.

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Step 3.1

Divide each term in $3 e^{x} = 15$ by $3$ .

$\frac{3 e^{x}}{3} = \frac{15}{3}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $3$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{3 e^{x}}{3} = \frac{15}{3}$

Step 3.2.1.2

Divide $e^{x}$ by $1$ .

$e^{x} = \frac{15}{3}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $15$ by $3$ .

$e^{x} = 5$

Step 4

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

$\ln (e^{x}) = \ln (5)$

Step 5

Expand the left side.

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Step 5.1

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

$x \ln (e) = \ln (5)$

Step 5.2

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

$x \cdot 1 = \ln (5)$

Step 5.3

Multiply $x$ by $1$ .

$x = \ln (5)$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \ln (5)$

Decimal Form:

$x = 1.60943791 \dots$