find the largest solution of the exponential equation 2^x^2= 4^ (7/2)x-3?

Question

A) -6
B) -1
C) 6
D) none of these
E) 1
i'm not sure if it's 6 or 1?

Answer 1

2^x² = 2²^(3.5x-3)

2^x² = 2^(7x-6)

x² = 7x-6

x² - 7x + 6 = 0
(x-6)(x-1) = 0
x =6, 1 so 6 is the largest [D]

Answer 2

2^x^2= 4^ (7/2)x-3
2^x^2= (2^2)^ (7/2)x-3
2^x^2= 2^2[(7/2)x-3]
2^x^2= 2^(7x-6)
x^2 = 7x - 6
x^2 - 7x + 6 =0
(x-1)(x-6) = 0
x = 1 or x = 6

Hence largest solution is 6, therefore answer is C

Answer 3

2^x^2= 4^ (7/2)x-3?

x^2=7x-6
x^2-7x+6=0
x1=1
x2=6

the largest solution is C) 6