Find the value of t for which \(\frac{64}{27} = (\frac{3}{4})^{t - 1}\)
MATHEMATICS
WAEC 1997
Find the value of t for which \(\frac{64}{27} = (\frac{3}{4})^{t - 1}\)
- A. -4
- B. -2
- C. 11/3
- D. 2
Correct Answer: B. -2
Explanation
\(\frac{64}{27} = (\frac{3}{4})^{t-1}\)
\((\frac{3}{4})^t = \frac{64}{27} \times \frac{3}{4} = \frac{16}{9}\)
\((\frac{3}{4})^t = (\frac{9}{16})^{-1}\)
\((\frac{3}{4})^t = (\frac{3}{4})^{-2}\)
t = -2
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