Find the value of t for which \(\frac{64}{27} = (\frac{3}{4})^{t - 1}\)
A
-4
B
-2
C
11/3
D
2
E
4
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
\(\frac{64}{27} = (\frac{3}{4})^{t-1}\)
\((\frac{3}{4})^t = \frac{64}{27} \times \frac{3}{4} = \frac{16}{9}\)
\((\frac{3}{4})^t = (\frac{9}{16})^{-1}\)
\((\frac{3}{4})^t = (\frac{3}{4})^{-2}\)
t = -2
Source: Myschool Past Questions Archive (Record #23882)