Asked by Julia
What are the possible solutions of 2log2a = 10 – 2log2b, where a and b are integers? Show you’re calculations
Answers
Answered by
Reiny
2log2a = 10 – 2log2b
I will assume you mean:
2log<sub>2</sub>a = 10 – 2log<sub>2</sub>b
log<sub>2</sub> a^2 + log<sub>2</sub> b^2 = 10
log<sub>2</sub> (a^2 b^2) = 10
a^2 b^2 = 2^10
ab = 2^5 = 32
So integer pairs of factors of 32 will work
(a,b) = {(1,32), (2,16), (4,8), (8,4), (16,2), (32,1)}
I will assume you mean:
2log<sub>2</sub>a = 10 – 2log<sub>2</sub>b
log<sub>2</sub> a^2 + log<sub>2</sub> b^2 = 10
log<sub>2</sub> (a^2 b^2) = 10
a^2 b^2 = 2^10
ab = 2^5 = 32
So integer pairs of factors of 32 will work
(a,b) = {(1,32), (2,16), (4,8), (8,4), (16,2), (32,1)}
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.