Finite Math Examples

$6 + 3 e^{x + 1} = 21$

Step 1

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

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Step 1.1

Subtract $6$ from both sides of the equation.

$3 e^{x + 1} = 21 - 6$

Step 1.2

Subtract $6$ from $21$ .

$3 e^{x + 1} = 15$

Step 2

Divide each term in $3 e^{x + 1} = 15$ by $3$ and simplify.

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Step 2.1

Divide each term in $3 e^{x + 1} = 15$ by $3$ .

$\frac{3 e^{x + 1}}{3} = \frac{15}{3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $3$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{3 e^{x + 1}}{3} = \frac{15}{3}$

Step 2.2.1.2

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

$e^{x + 1} = \frac{15}{3}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $15$ by $3$ .

$e^{x + 1} = 5$

Step 3

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

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

Step 4

Expand the left side.

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Step 4.1

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

$(x + 1) \ln (e) = \ln (5)$

Step 4.2

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

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

Step 4.3

Multiply $x + 1$ by $1$ .

$x + 1 = \ln (5)$

Step 5

Subtract $1$ from both sides of the equation.

$x = \ln (5) - 1$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \ln (5) - 1$

Decimal Form:

$x = 0.60943791 \dots$