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

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

Step 1

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

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

Step 2

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

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

Step 3

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

$x + 3 = - 1$

Step 4

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

Subtract $3$ from both sides of the equation.

$x = - 1 - 3$

Subtract $3$ from $- 1$ .

$x = - 4$