If (25)\(^{x - 1}\) = 64(\(\frac{5}{2}\))\(^6\), then x has the value
A
7
B
4
C
32
D
64
E
5
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
(25)\(^{x - 1}\) = 64(\(\frac{5}{2}\))\(^6\)
(\(\frac{5}{2}\))\(^6\) = (\(\frac{5^6}{64}\))
25\(^{x - 1}\) = 64 x (\(\frac{5^6}{64}\))
5\(^{2x - 2}\) = 5\(^6\)
2x - 2 = 6
= \(\frac{8}{2}\)
= 4
Source: Myschool Past Questions Archive (Record #32718)