Solve for x 5^(3x)=1/125

$5^{3 x} = \frac{1}{125}$

Step 1

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

$5^{3 x} = \frac{1}{125^{1}}$

Step 2

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

$5^{3 x} = 125^{- 1}$

Step 3

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

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

Step 4

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

$3 x = - 3$

Step 5

Divide each term in $3 x = - 3$ by $3$ and simplify.

Divide each term in $3 x = - 3$ by $3$ .

$\frac{3 x}{3} = \frac{- 3}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 3}{3}$

Divide $x$ by $1$ .

$x = \frac{- 3}{3}$

Simplify the right side.

Divide $- 3$ by $3$ .

$x = - 1$