Library / /72 of 310

, 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 $\frac{1}{2}(a+b)=3$ .

Want a route through all this instead of an archive? The track puts 2,444 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.