The first step for solving this equation is to write [tex]25^{x+2} [/tex] in exponential form with a base of 5.
[tex]5^{2x+4} [/tex] = [tex]( \frac{1}{5}) ^{4x} [/tex]
Write [tex]( \frac{1}{5}) ^{4x} [/tex] in exponential form with a base of 5.
[tex]5^{2x+4} [/tex] = [tex]5^{-4x} [/tex]
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 = [tex]- \frac{2}{3} [/tex]
Let me know if you have any further questions.
:)
