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Solve the log problem.

log[(a+b)/3] = (log a + log b)/3, then a/b + b/a =

Note by Abhishek Mohapatra
3 years, 11 months ago

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How do we get the integer solutions ????? Abhishek Mohapatra · 3 years, 11 months ago

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it appears to be a very easy question......:) here is the probable solution....: log[(a+b)/3]=(log a+log b)/3
=>log[(a+b)/3]=log(ab)/3
=>3
log[(a+b)/3]=log(ab)
=>log[{(a+b)/3}^3]=log(a
b)...........taking antilog,....... =>[(a+b)^3]/[27]=ab
=>a^3+b^3+3
ab(a+b)=27ab
=>so the integer solutions are [a=2 & b=4] ; [a=4 &b=-16] ; [a=4 & b=2].....BUT YOU SEE "b" CAN NOT TAKE NEGATIVE VALUE INSIDE LOGARITHM.....SO THE SOLUTION SHOULD BE.....[a=2 & b=4] AND [a=4 & b=2].......................... HOPE THIS HELPS.........:)) Raja Metronetizen · 3 years, 11 months ago

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@Raja Metronetizen how did you directly deduce the integer solns from the step:=>a^3+b^3+3ab(a+b)=27ab Bhargav Das · 3 years, 11 months ago

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@Bhargav Das ha ha....!! ...i thought if anyone asks me that step by step solution.....i would crumble....!!!.....then to find the solution of a^3+b^3+3ab(a+b)=27ab i only put my graphing knowledge.........BUT EASY TO SAY YOU MAY FIND THE SOLUTION WITHOUT APPLYING YOUR BRAIN EVEN BY CLICKING HERE SIMPLY.......i only used this website to check my answer whether it is right or wrong......:-) Raja Metronetizen · 3 years, 11 months ago

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@Raja Metronetizen How do we get the integer solutions ????? Abhishek Mohapatra · 3 years, 11 months ago

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