Calculus Examples

$2^{x + 2} = \frac{1}{8}$

Step 1

Raise $8$ to the power of $1$ .

$2^{x + 2} = \frac{1}{8^{1}}$

Step 2

Move $8^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$2^{x + 2} = 8^{- 1}$

Step 3

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

$2^{x + 2} = 2^{- 3}$

Step 4

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

$x + 2 = - 3$

Step 5

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

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Step 5.1

Subtract $2$ from both sides of the equation.

$x = - 3 - 2$

Step 5.2

Subtract $2$ from $- 3$ .

$x = - 5$