SOLUTION: if a=b^x, b=c^y, c=a^z then find the value of xyz

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Question 763652: if a=b^x, b=c^y, c=a^z then find the value of xyz
Answer by ramkikk66(644) About Me  (Show Source):
You can put this solution on YOUR website!

Let's start from the 1st equation and keep expanding it.

Remember the identity: highlight%28%28x%5Em%29%5En+=+x%5E%28m%2An%29%29

a+=+b%5Ex

a+=+%28c%5Ey%29%5Ex    ===> since b = c^y

So a+=+c%5E%28x%2Ay%29 

Since c = a^z,

a+=+%28a%5Ez%29%5E%28x%2Ay%29+=+a%5E%28x%2Ay%2Az%29

So x%2Ay%2Az+=+1

Hope this helps. Please mail me if it's still not clear.

:)