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

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