Trigonometry Examples

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

Step 1

Move $e^{x}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 2

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

$- x = 1 - x$

Step 3

Solve for $x$ .

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Step 3.1

Move all terms containing $x$ to the left side of the equation.

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Step 3.1.1

Add $x$ to both sides of the equation.

$- x + x = 1$

Step 3.1.2

Add $- x$ and $x$ .

$0 = 1$

Step 3.2

Since $0 \neq 1$ , there are no solutions.

No solution