Calculus Examples

$e^{- \frac{1}{x}} = e^{\frac{1}{6}}$

Step 1

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

$e^{- \frac{1}{x}} = e^{\frac{1}{6}}$

Step 2

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

$- \frac{1}{x} = \frac{1}{6}$

Step 3

Solve for $x$ .

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Step 3.1

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

$- 1 \cdot 6 = x \cdot 1$

Step 3.2

Solve the equation for $x$ .

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Step 3.2.1

Rewrite the equation as $x \cdot 1 = - 1 \cdot 6$ .

$x \cdot 1 = - 1 \cdot 6$

Step 3.2.2

Multiply $x$ by $1$ .

$x = - 1 \cdot 6$

Step 3.2.3

Multiply $- 1$ by $6$ .

$x = - 6$