how do you solve 25^x2 * 5^5x = 125

Answer 1

Make everything base 5. Since 25=5^2 and 125 = 5^3, we have
25^x^2 * 5^5x = 125
5^(2x^2) * 5^(5x) = 5^3
2x^2+5x-3 = 0
Now just solve the quadratic as usual.