SOLUTION: if 16=6^x, 27=(12)^y find three integer numbers (a, b, c,) satisfy. (x+a) (y+b) =c

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Question 1150780: if 16=6^x, 27=(12)^y find three integer numbers (a, b, c,)
satisfy. (x+a) (y+b) =c

Found 2 solutions by ikleyn, Edwin McCravy:
Answer by ikleyn(52790)   (Show Source): You can put this solution on YOUR website!



Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
     

Substitute in




To make that come out an integer, all the ln's must cancel out,
plus both denominators must cancel into both numerators.

The coefficient of the first ln in the right denominator is twice
the coefficient of the second ln.

Therefore, the right denominator will cancel into the left numerator if
the coefficient 4+a is twice the coefficient a. So to have that,
4+a = 2a
  4 = a

The coefficient of both ln's in the left denominator are equal,

Therefore, the left denominator will cancel into the right numerator if 
coefficients 3+b and 2b are equal.  So to have that,
3+b = 2b
  3 = b

So substituting a = 4 and b = 3



So a = 3, b = 4, and c = 24

Edwin


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