Algebra Examples

$e^{5 - 2 p} + 2 = 4$

Step 1

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

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Step 1.1

Subtract $2$ from both sides of the equation.

$e^{5 - 2 p} = 4 - 2$

Step 1.2

Subtract $2$ from $4$ .

$e^{5 - 2 p} = 2$

Step 2

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

$\ln (e^{5 - 2 p}) = \ln (2)$

Step 3

Expand the left side.

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Step 3.1

Expand $\ln (e^{5 - 2 p})$ by moving $5 - 2 p$ outside the logarithm.

$(5 - 2 p) \ln (e) = \ln (2)$

Step 3.2

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

$(5 - 2 p) \cdot 1 = \ln (2)$

Step 3.3

Multiply $5 - 2 p$ by $1$ .

$5 - 2 p = \ln (2)$

Step 4

Subtract $5$ from both sides of the equation.

$- 2 p = \ln (2) - 5$

Step 5

Divide each term in $- 2 p = \ln (2) - 5$ by $- 2$ and simplify.

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Step 5.1

Divide each term in $- 2 p = \ln (2) - 5$ by $- 2$ .

$\frac{- 2 p}{- 2} = \frac{\ln (2)}{- 2} + \frac{- 5}{- 2}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 2$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{- 2 p}{- 2} = \frac{\ln (2)}{- 2} + \frac{- 5}{- 2}$

Step 5.2.1.2

Divide $p$ by $1$ .

$p = \frac{\ln (2)}{- 2} + \frac{- 5}{- 2}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Simplify each term.

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Step 5.3.1.1

Move the negative in front of the fraction.

$p = - \frac{\ln (2)}{2} + \frac{- 5}{- 2}$

Step 5.3.1.2

Dividing two negative values results in a positive value.

$p = - \frac{\ln (2)}{2} + \frac{5}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$p = - \frac{\ln (2)}{2} + \frac{5}{2}$

Decimal Form:

$p = 2.15342640 \dots$