Precalculus Examples

$4 e^{x + 1} = 5$

Step 1

Divide each term in $4 e^{x + 1} = 5$ by $4$ and simplify.

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Step 1.1

Divide each term in $4 e^{x + 1} = 5$ by $4$ .

$\frac{4 e^{x + 1}}{4} = \frac{5}{4}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $4$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{4 e^{x + 1}}{4} = \frac{5}{4}$

Step 1.2.1.2

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

$e^{x + 1} = \frac{5}{4}$

Step 2

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

$\ln (e^{x + 1}) = \ln (\frac{5}{4})$

Step 3

Expand the left side.

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Step 3.1

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

$(x + 1) \ln (e) = \ln (\frac{5}{4})$

Step 3.2

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

$(x + 1) \cdot 1 = \ln (\frac{5}{4})$

Step 3.3

Multiply $x + 1$ by $1$ .

$x + 1 = \ln (\frac{5}{4})$

Step 4

Subtract $1$ from both sides of the equation.

$x = \ln (\frac{5}{4}) - 1$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \ln (\frac{5}{4}) - 1$

Decimal Form:

$x = - 0.77685644 \dots$