SOLUTION: 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

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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): You can put this solution on YOUR website!
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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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