Solve for x 1/125=25^(x+5)

$\frac{1}{125} = 25^{x + 5}$

Rewrite the equation as $25^{x + 5} = \frac{1}{125}$ .

$25^{x + 5} = \frac{1}{125}$

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

$25^{x + 5} = \frac{1}{125^{1}}$

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

$25^{x + 5} = 125^{- 1}$

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

$5^{2 (x + 5)} = 5^{- 3}$

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

$2 (x + 5) = - 3$

Solve for $x$ .

Divide each term in $2 (x + 5) = - 3$ by $2$ and simplify.

Divide each term in $2 (x + 5) = - 3$ by $2$ .

$\frac{2 (x + 5)}{2} = \frac{- 3}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 (x + 5)}{2} = \frac{- 3}{2}$

Divide $x + 5$ by $1$ .

$x + 5 = \frac{- 3}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$x + 5 = - \frac{3}{2}$

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

Subtract $5$ from both sides of the equation.

$x = - \frac{3}{2} - 5$

To write $- 5$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x = - \frac{3}{2} - 5 \cdot \frac{2}{2}$

Combine $- 5$ and $\frac{2}{2}$ .

$x = - \frac{3}{2} + \frac{- 5 \cdot 2}{2}$

Combine the numerators over the common denominator.

$x = \frac{- 3 - 5 \cdot 2}{2}$

Simplify the numerator.

Multiply $- 5$ by $2$ .

$x = \frac{- 3 - 10}{2}$

Subtract $10$ from $- 3$ .

$x = \frac{- 13}{2}$

Move the negative in front of the fraction.

$x = - \frac{13}{2}$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{13}{2}$

Decimal Form:

$x = - 6.5$

Mixed Number Form:

$x = - 6 \frac{1}{2}$

Solve for x 1/125=25^(x+5)

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