Posted by **hemant** on Friday, May 24, 2013 at 5:30am.

x and y are positive real numbers that satisfy logxy+logyx=174 and xy=2883√. If x+y=a+bc√, where a, b and c are positive integers and c is not divisible by the square of any prime, what is the value of a+b+c?

- maths -
**Reiny**, Friday, May 24, 2013 at 7:59am
Having posted the same problem three times and not

getting a response should have given you a hint, that there might be something wrong with the question, or the way you typed it.

e.g. 2883√ makes no sense, the √ is not written behind the number

which makes x+y = a + bc√ completely ambiguous.

I will start it off:

logxy+logyx=174

the way you typed it .....

2 log xy = 174

log xy = 72

xy = 10^72 ---- huge!!

but assuming xy = √2883

so √2883 = 10^72 ??? , not likely

I have a feeling you meant:

log_{x}y + log_{y}x = 174

- maths -
**hemant**, Friday, May 24, 2013 at 12:20pm
logxy + logyx = 17/4

- maths -
**hemant**, Friday, May 24, 2013 at 12:20pm
log y base x + log x base y =17/4

sorry for the typo.

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