Question

25^(2x)=5^(x^2-12)

Answer 1

(x-6)(x+2)

Answer 2

Change it into this equation
(5^2)^(2x)=5^(x^2-12)

Answer 3

therefore x=6 or x=-2

Answer 4

25 = 5^2
left side (5^2)^(2x) then multiply exponents and get 5^4x

Answer 5

if 5^4x = 5^(x^2-12) since the bases are the same you just have
4x = x^2 - 12, now factor or use the quadratic formula

Answer 6

25^(2x)=5^(x^2-12)
5^4x = 5^(x^2-12)
we have the same base 5 therefore
\[4x=x^2-12\]
\[0=x^2-4x-12\]
\[0=(x-6)(x+2)\]
x-6=0
x=6

x+2=0
x=-2