Find $x$: $\left(\dfrac{3}{4}\right)^{x} = \dfrac{16}{9}$.

Find $x$: $\left(\dfrac{3}{4}\right)^{x} = \dfrac{16}{9}$.
  1. $2$
  2. $-2$
  3. $-\dfrac{1}{2}$
  4. $\dfrac{1}{2}$

Solution

$\dfrac{16}{9} = \left(\dfrac{4}{3}\right)^{2} = \left(\dfrac{3}{4}\right)^{-2}$. So $x = -2$.

Asked in: IMO

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