Solve for x 2^(x-3)=1/32

$2^{x - 3} = \frac{1}{32}$

Step 1

Raise $32$ to the power of $1$ .

$2^{x - 3} = \frac{1}{32^{1}}$

Step 2

Move $32^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$2^{x - 3} = 32^{- 1}$

Step 3

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

$2^{x - 3} = 2^{- 5}$

Step 4

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

$x - 3 = - 5$

Step 5

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

Add $3$ to both sides of the equation.

$x = - 5 + 3$

Add $- 5$ and $3$ .

$x = - 2$