Precalculus Examples

$- 7 e^{n - 8} = - 46$

Step 1

Divide each term in $- 7 e^{n - 8} = - 46$ by $- 7$ and simplify.

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Step 1.1

Divide each term in $- 7 e^{n - 8} = - 46$ by $- 7$ .

$\frac{- 7 e^{n - 8}}{- 7} = \frac{- 46}{- 7}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $- 7$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{- 7 e^{n - 8}}{- 7} = \frac{- 46}{- 7}$

Step 1.2.1.2

Divide $e^{n - 8}$ by $1$ .

$e^{n - 8} = \frac{- 46}{- 7}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Dividing two negative values results in a positive value.

$e^{n - 8} = \frac{46}{7}$

Step 2

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

$\ln (e^{n - 8}) = \ln (\frac{46}{7})$

Step 3

Expand the left side.

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Step 3.1

Expand $\ln (e^{n - 8})$ by moving $n - 8$ outside the logarithm.

$(n - 8) \ln (e) = \ln (\frac{46}{7})$

Step 3.2

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

$(n - 8) \cdot 1 = \ln (\frac{46}{7})$

Step 3.3

Multiply $n - 8$ by $1$ .

$n - 8 = \ln (\frac{46}{7})$

Step 4

Add $8$ to both sides of the equation.

$n = \ln (\frac{46}{7}) + 8$

Step 5

The result can be shown in multiple forms.

Exact Form:

$n = \ln (\frac{46}{7}) + 8$

Decimal Form:

$n = 9.88273124 \dots$