Solve for x 25^x=1/5

$25^{x} = \frac{1}{5}$

Step 1

Raise $5$ to the power of $1$ .

$25^{x} = \frac{1}{5^{1}}$

Step 2

Move $5^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$25^{x} = 5^{- 1}$

Step 3

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

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

Step 4

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

$2 x = - 1$

Step 5

Divide each term in $2 x = - 1$ by $2$ and simplify.

Divide each term in $2 x = - 1$ by $2$ .

$\frac{2 x}{2} = \frac{- 1}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 1}{2}$

Divide $x$ by $1$ .

$x = \frac{- 1}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{1}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{1}{2}$

Decimal Form:

$x = - 0.5$