Solve for x Solve 1/25=5^(x+4)

Solve $\frac{1}{25} = 5^{x + 4}$

Rewrite the equation as $5^{x + 4} = \frac{1}{25}$ .

$5^{x + 4} = \frac{1}{25}$

Raise $25$ to the power of $1$ .

$5^{x + 4} = \frac{1}{25^{1}}$

Move $25^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$5^{x + 4} = 25^{- 1}$

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

$5^{x + 4} = 5^{- 2}$

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

$x + 4 = - 2$

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

Subtract $4$ from both sides of the equation.

$x = - 2 - 4$

Subtract $4$ from $- 2$ .

$x = - 6$