Algebra Examples

$\frac{e^{3 x + 2}}{e^{x}} = 1$

Step 1

Cancel the common factor of $e^{3 x + 2}$ and $e^{x}$ .

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Step 1.1

Factor $e^{x}$ out of $e^{3 x + 2}$ .

$\frac{e^{x} e^{2 x + 2}}{e^{x}} = 1$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Multiply by $1$ .

$\frac{e^{x} e^{2 x + 2}}{e^{x} \cdot 1} = 1$

Step 1.2.2

Cancel the common factor.

$\frac{e^{x} e^{2 x + 2}}{e^{x} \cdot 1} = 1$

Step 1.2.3

Rewrite the expression.

$\frac{e^{2 x + 2}}{1} = 1$

Step 1.2.4

Divide $e^{2 x + 2}$ by $1$ .

$e^{2 x + 2} = 1$

Step 2

Solve for $x$ .

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Step 2.1

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

$\ln (e^{2 x + 2}) = \ln (1)$

Step 2.2

Expand the left side.

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Step 2.2.1

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

$(2 x + 2) \ln (e) = \ln (1)$

Step 2.2.2

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

$(2 x + 2) \cdot 1 = \ln (1)$

Step 2.2.3

Multiply $2 x + 2$ by $1$ .

$2 x + 2 = \ln (1)$

Step 2.3

Simplify the right side.

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Step 2.3.1

The natural logarithm of $1$ is $0$ .

$2 x + 2 = 0$

Step 2.4

Subtract $2$ from both sides of the equation.

$2 x = - 2$

Step 2.5

Divide each term in $2 x = - 2$ by $2$ and simplify.

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Step 2.5.1

Divide each term in $2 x = - 2$ by $2$ .

$\frac{2 x}{2} = \frac{- 2}{2}$

Step 2.5.2

Simplify the left side.

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Step 2.5.2.1

Cancel the common factor of $2$ .

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Step 2.5.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 2}{2}$

Step 2.5.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 2}{2}$

Step 2.5.3

Simplify the right side.

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Step 2.5.3.1

Divide $- 2$ by $2$ .

$x = - 1$