The first step for solving this equation is to write
![25^{x+2}](https://tex.z-dn.net/?f=25%5E%7Bx%2B2%7D%20)
in exponential form with a base of 5.
![5^{2x+4}](https://tex.z-dn.net/?f=5%5E%7B2x%2B4%7D%20)
=
![( \frac{1}{5}) ^{4x}](https://tex.z-dn.net/?f=%28%20%5Cfrac%7B1%7D%7B5%7D%29%20%5E%7B4x%7D%20%20)
Write
![( \frac{1}{5}) ^{4x}](https://tex.z-dn.net/?f=%28%20%5Cfrac%7B1%7D%7B5%7D%29%20%5E%7B4x%7D%20)
in exponential form with a base of 5.
![5^{2x+4}](https://tex.z-dn.net/?f=5%5E%7B2x%2B4%7D%20)
=
![5^{-4x}](https://tex.z-dn.net/?f=5%5E%7B-4x%7D%20)
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}](https://tex.z-dn.net/?f=-%20%5Cfrac%7B2%7D%7B3%7D%20)
Let me know if you have any further questions.
:)