Question 1034317: Please help me solve this question
Solve the system; logx base a.log ( xyz ) base a = 48
Logy base a.log ( xyz ) base a = 12, a > 0, a is not = to 1
Logz base a.log ( xyz ) base a = 84
Answer by ikleyn(52781)   (Show Source):
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Please help me solve this question
Solve the system; logx base a.log ( xyz ) base a = 48,
Logy base a.log ( xyz ) base a = 12,
Logz base a.log ( xyz ) base a = 84,
a > 0, a is not = to 1
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 =  , (1)
 =  , (2)
 =  . (3)
Add (1), (2) and (3) (both sides). You will get
 = 48 + 12 + 84 = 144.
Hence,  = +/- 12.
Now, consider two cases.
a) = + 12.
Then  =  = 4 ---> x =  ,
 =  = 1 ---> y =  ,
 =  = 7 ---> z =  .
b) = - 12.
Then =  = -4 ---> x =  ,
=  = -1 ---> y =  ,
=  = -7 ---> z =  .
Thus you have two solutions (or two sets of solutions).
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