Mathematics

Find the value of t for which (frac{64}{27} = (frac{3}{4})^{t – 1})

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
Correct Answer: Option B
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