SOLUTION: Respected Sir/Madam , Please help me to solve my problem . I Will be very grateful for your help. My question is : If (log a)/(y-z) =(log b)/ (z-x)=(log c) / (x-y) then what is t

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Respected Sir/Madam , Please help me to solve my problem . I Will be very grateful for your help. My question is : If (log a)/(y-z) =(log b)/ (z-x)=(log c) / (x-y) then what is t      Log On


   



Question 479519: Respected Sir/Madam ,
Please help me to solve my problem . I Will be very grateful for your help. My question is :
If (log a)/(y-z) =(log b)/ (z-x)=(log c) / (x-y) then what is the value of a^(y+z) * b ^ (z+x) *c^(x+y)
As the Answer given is :1
So please Sir/Madam provide me the steps for this question..
Thank you,

Answer by Tatiana_Stebko(1539) About Me  (Show Source):
You can put this solution on YOUR website!
1. +%28log+a%29%2F%28y-z%29+=%28log+b%29%2F+%28z-x%29=%28log+c%29+%2F+%28x-y%29 or

Use formula n%2Aloga=log%28a%5En%29

+a%5E%281%2F%28y-z%29%29+=+b%5E%281%2F+%28z-x%29%29=c%5E%281+%2F+%28x-y%29%29
So +a%5E%281%2F%28y-z%29%29+=+b%5E%281%2F+%28z-x%29%29 then %28+a%5E%281%2F%28y-z%29%29%29%5E%28z-x%29+=+%28b%5E%281%2F+%28z-x%29%29%29%5E%28z-x%29 => b=a%5E%28%28z-x%29%2F%28y-z%29%29
+a%5E%281%2F%28y-z%29%29=c%5E%281+%2F+%28x-y%29%29, then +%28a%5E%281%2F%28y-z%29%29%29%5E%28x-y%29+=%28c%5E%281+%2F+%28x-y%29%29%29%5E%28x-y%29 => c=a%5E%28%28x-y%29%2F%28y-z%29%29
.
2.