How do I prove that ab+5(a-b)=1 If log_(12)18=a and log_(24)54=b then how do I prove ab+5(a−b)=1?

piopiopioirp

piopiopioirp

Answered question

2022-11-09

How do I prove that a b + 5 ( a b ) = 1
If log 12 18 = a and log 24 54 = b then how do I prove a b + 5 ( a b ) = 1?
I figured that out it's log a b and log 2 a 3 b but how do I solve it?

Answer & Explanation

Milton Gilmore

Milton Gilmore

Beginner2022-11-10Added 20 answers

12 a = 18 , 24 b = 54 24 b 12 a = 3 2 3 b 3 b 2 2 a 3 a = 3 2 3 b 2 a = 3 1 + a b ( 3 b 2 a ) ln 2 = ( 1 + a b ) ln 3. This is what I preliminarily got. More on this later for you.What you need to prove is: a = 5 b + 1 b + 5 .Can you use my hint to connect with the answer?

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