Question

For what values of x does
25^x = 5^(x2-3?)

Answer 1

x = 3 or x = -1

Explanation:

25^x = 5^(x^2 - 3)

<=> (5^2)^x = 5^(x^2 - 3)

<=> 5^(2x) = 5^(x^2 - 3)

<=> 2x = x^2 - 3

<=> x^2 - 2x - 3 = 0

<=> x^2 + x - 3x - 3 = 0

<=> x(x + 1) - 3(x + 1) = 0

<=> (x - 3)(x + 1) = 0

<=> x = 3 or x = -1

I hope this helps!