Question

What are the possible solutions of 2 log base 2 𝒂 = 10 − 2 log base 2 𝒃, where 𝒂 and 𝒃 are integers? Show work.

Answer 1

assuming base 2, we have
2loga = 10 - 2logb
2(loga + logb) = 10
loga + logb = 5
log(ab) = 5
ab = 2^5 = 32
So, what are the factors of 32?

Answer 2

Factors of 32 are 1, 2, 4, 8, 16, 32

Answer 3

so, those are possible values for a and b. Just pair them up so that ab=32

Answer 4

oh ok thank you!