CEMC Fermat, 2012

Algebra Difficulty 1.4 Junior Find the answer Canada

If $(2^a)(2^b)=64$ , then the mean (average) of $a$ and $b$ is

Pick one

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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