Find $x$: $8^{x} \cdot 4^{x} = 16^{5}$.

Find $x$: $8^{x} \cdot 4^{x} = 16^{5}$.
  1. $2$
  2. $3$
  3. $4$
  4. $5$

Solution

Base 2: $(2^{3})^{x} \cdot (2^{2})^{x} = (2^{4})^{5} \Rightarrow 2^{5x} = 2^{20} \Rightarrow x = 4$.

Asked in: IMO

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