Solve for x 5^(x-2)=1/125

$5^{x - 2} = \frac{1}{125}$

Step 1

Raise $125$ to the power of $1$ .

$5^{x - 2} = \frac{1}{125^{1}}$

Step 2

Move $125^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$5^{x - 2} = 125^{- 1}$

Step 3

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

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

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.

Add $2$ to both sides of the equation.

$x = - 3 + 2$

Add $- 3$ and $2$ .

$x = - 1$