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.