Precalculus Examples

3 e^{- 5 x} = 132

$3 e^{- 5 x} = 132$

Step 1

Divide each term in

3 e^{- 5 x} = 132

$3 e^{- 5 x} = 132$ by

3

$3$ and simplify.

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Step 1.1

Divide each term in

3 e^{- 5 x} = 132

$3 e^{- 5 x} = 132$ by

3

$3$ .

\frac{3 e^{- 5 x}}{3} = \frac{132}{3}

$\frac{3 e^{- 5 x}}{3} = \frac{132}{3}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of

3

$3$ .

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Step 1.2.1.1

Cancel the common factor.

\frac{3 e^{- 5 x}}{3} = \frac{132}{3}

$\frac{3 e^{- 5 x}}{3} = \frac{132}{3}$

Step 1.2.1.2

Divide

e^{- 5 x}

$e^{- 5 x}$ by

1

$1$ .

e^{- 5 x} = \frac{132}{3}

$e^{- 5 x} = \frac{132}{3}$

e^{- 5 x} = \frac{132}{3}

$e^{- 5 x} = \frac{132}{3}$

e^{- 5 x} = \frac{132}{3}

$e^{- 5 x} = \frac{132}{3}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide

132

$132$ by

3

$3$ .

e^{- 5 x} = 44

$e^{- 5 x} = 44$

e^{- 5 x} = 44

$e^{- 5 x} = 44$

e^{- 5 x} = 44

$e^{- 5 x} = 44$

Step 2

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

\ln (e^{- 5 x}) = \ln (44)

$\ln (e^{- 5 x}) = \ln (44)$

Step 3

Expand the left side.

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Step 3.1

Expand

\ln (e^{- 5 x})

$\ln (e^{- 5 x})$ by moving

- 5 x

$- 5 x$ outside the logarithm.

- 5 x \ln (e) = \ln (44)

$- 5 x \ln (e) = \ln (44)$

Step 3.2

The natural logarithm of

e

$e$ is

1

$1$ .

- 5 x \cdot 1 = \ln (44)

$- 5 x \cdot 1 = \ln (44)$

Step 3.3

Multiply

- 5

$- 5$ by

1

$1$ .

- 5 x = \ln (44)

$- 5 x = \ln (44)$

- 5 x = \ln (44)

$- 5 x = \ln (44)$

Step 4

Divide each term in

- 5 x = \ln (44)

$- 5 x = \ln (44)$ by

- 5

$- 5$ and simplify.

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Step 4.1

Divide each term in

- 5 x = \ln (44)

$- 5 x = \ln (44)$ by

- 5

$- 5$ .

\frac{- 5 x}{- 5} = \frac{\ln (44)}{- 5}

$\frac{- 5 x}{- 5} = \frac{\ln (44)}{- 5}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of

- 5

$- 5$ .

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Step 4.2.1.1

Cancel the common factor.

\frac{- 5 x}{- 5} = \frac{\ln (44)}{- 5}

$\frac{- 5 x}{- 5} = \frac{\ln (44)}{- 5}$

Step 4.2.1.2

Divide

x

$x$ by

1

$1$ .

x = \frac{\ln (44)}{- 5}

$x = \frac{\ln (44)}{- 5}$

x = \frac{\ln (44)}{- 5}

$x = \frac{\ln (44)}{- 5}$

x = \frac{\ln (44)}{- 5}

$x = \frac{\ln (44)}{- 5}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Move the negative in front of the fraction.

x = - \frac{\ln (44)}{5}

$x = - \frac{\ln (44)}{5}$

x = - \frac{\ln (44)}{5}

$x = - \frac{\ln (44)}{5}$

x = - \frac{\ln (44)}{5}

$x = - \frac{\ln (44)}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

x = - \frac{\ln (44)}{5}

$x = - \frac{\ln (44)}{5}$

Decimal Form:

x = - 0.75683792 \dots

$x = - 0.75683792 \dots$

[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$