Finite Math Examples

$y = e^{- x} - e$

Step 1

Set $e^{- x} - e$ equal to $0$ .

$e^{- x} - e = 0$

Step 2

Solve for $x$ .

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Step 2.1

Add $e$ to both sides of the equation.

$e^{- x} = e$

Step 2.2

Create equivalent expressions in the equation that all have equal bases.

$e^{- x} = e^{1}$

Step 2.3

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$- x = 1$

Step 2.4

Divide each term in $- x = 1$ by $- 1$ and simplify.

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Step 2.4.1

Divide each term in $- x = 1$ by $- 1$ .

$\frac{- x}{- 1} = \frac{1}{- 1}$

Step 2.4.2

Simplify the left side.

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Step 2.4.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{1}{- 1}$

Step 2.4.2.2

Divide $x$ by $1$ .

$x = \frac{1}{- 1}$

Step 2.4.3

Simplify the right side.

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Step 2.4.3.1

Divide $1$ by $- 1$ .

$x = - 1$

Step 3