Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 2.0 Junior Find the answer

If $(2^{a})(2^{b})=64$ , what is the mean (average) of $a$ and $b$ ?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Since $(2^{a})(2^{b})=64$ , then $2^{a+b}=64$ , using an exponent law. Since $64=2^{6}$ , then $2^{a+b}=2^{6}$ and so $a+b=6$ . Therefore, the average of $a$ and $b$ is $\frac{1}{2}(a+b)=3$ .

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