Solve $\left(\dfrac{2}{3}\right)^{x-1} = \dfrac{27}{8}$.

Solve $\left(\dfrac{2}{3}\right)^{x-1} = \dfrac{27}{8}$.
  1. $-2$
  2. $-3$
  3. $2$
  4. $4$

Solution

$\dfrac{27}{8} = \left(\dfrac{3}{2}\right)^{3} = \left(\dfrac{2}{3}\right)^{-3}$. So $x - 1 = -3 \Rightarrow x = -2$.

Asked in: IMO

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