Question

25^(x+2) = (1/5)^(4x)

Answer 1

The first step for solving this equation is to write $25^{x+2}$ in exponential form with a base of 5.
$5^{2x+4}$ = $( \frac{1}{5}) ^{4x}$
Write $( \frac{1}{5}) ^{4x}$ in exponential form with a base of 5.
$5^{2x+4}$ = $5^{-4x}$
Since the bases on both sides of the equal are the same,, set the exponents equal.
2x + 4 = -4x
Move the constant to the right side of the equation and then change its sign.
2x = -4x - 4
Now move the variable to the left side and change its sign.
2x + 4x = -4
Collect the terms with an x variable.
6x = -4
Lastly,, divide both sides of the equation by 6 to get your final answer.
x = $- \frac{2}{3}$
Let me know if you have any further questions.
:)