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If 4^a =8 ^b , what is the ratio of a to b?
  1. 1/2
  2. 2/3
  3. 3/2
  4. None of these
Explanation

If, find the ratio abfrac{a}{b}

Write both sides with base 2:


4^a = (2^2)^a = 2^{2a} \ 8^b = (2^3)^b = 2^{3b} Rightarrow 2^{2a} = 2^{3b} Rightarrow 2a = 3b Rightarrow frac{a}{b} = frac{3}{2}

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