25^(6-x^2) = (1/5)^2 x

Question

solve this equations

Answer 1

You need to re-write each side of the equation such that the base is 5.

 

25 = 5² and 1/5 = 5^-1

 

This problem now becomes:

 

(5²)^{6 - x²} = (5^-1)^2x

 

5^{(12 - 2x²) =} 5^-2x

 

If the bases are even, then we can set the exponents equal to each other. 

 

12 - 2x² = -2x

12 + 2x - 2x² = 0

6 + x - x² = 0

(3 - x)(2 + x) = 0

x = 3 or x = -2