Precalculus Examples

$- 4 e^{p - 1} - 5 = - 96$

Step 1

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

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Step 1.1

Add $5$ to both sides of the equation.

$- 4 e^{p - 1} = - 96 + 5$

Step 1.2

Add $- 96$ and $5$ .

$- 4 e^{p - 1} = - 91$

Step 2

Divide each term in $- 4 e^{p - 1} = - 91$ by $- 4$ and simplify.

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Step 2.1

Divide each term in $- 4 e^{p - 1} = - 91$ by $- 4$ .

$\frac{- 4 e^{p - 1}}{- 4} = \frac{- 91}{- 4}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 4$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 4 e^{p - 1}}{- 4} = \frac{- 91}{- 4}$

Step 2.2.1.2

Divide $e^{p - 1}$ by $1$ .

$e^{p - 1} = \frac{- 91}{- 4}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Dividing two negative values results in a positive value.

$e^{p - 1} = \frac{91}{4}$

Step 3

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

$\ln (e^{p - 1}) = \ln (\frac{91}{4})$

Step 4

Expand the left side.

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Step 4.1

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

$(p - 1) \ln (e) = \ln (\frac{91}{4})$

Step 4.2

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

$(p - 1) \cdot 1 = \ln (\frac{91}{4})$

Step 4.3

Multiply $p - 1$ by $1$ .

$p - 1 = \ln (\frac{91}{4})$

Step 5

Add $1$ to both sides of the equation.

$p = \ln (\frac{91}{4}) + 1$

Step 6

The result can be shown in multiple forms.

Exact Form:

$p = \ln (\frac{91}{4}) + 1$

Decimal Form:

$p = 4.12456514 \dots$