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If a^x=b b^y=c c^z=a Prove xyz=1 Please give the solution

  • If
  • a^x=b
  • b^y=c
  • c^z=a
  • Prove xyz=1
  • Please give the solution

Grade:11

6 Answers

Rinkoo Gupta
askIITians Faculty 80 Points
8 years ago

ax=b => x=logab

by=c=> y=logbc

cz=a=> z=logca

xyz=(logab.logbc).logca

=logac.logca

=logaa

=1

Thanks & Regards

Rinkoo Gupta

AskIITians Faculty

Sher Mohammad IIT Delhi
askIITians Faculty 174 Points
8 years ago
a^xyz
=(a^x)^yz
=b^yz
=(b^y)^z
=c^z
=a
by comparision xyz=1 proved

Sher Mohammad
faculty askiitians
pramod Gopinath
25 Points
8 years ago
a^x=b
b^y=c =>a^xy=c
c^z=a =>a^xyz=a =>xyz=1
Swati Kohli
34 Points
7 years ago
In equation:
 
       a^x=b             (put value of a i.e. c^z)
=>   c^z(x)=b
 
Now, put value for c i.e. b^y
 
=>   b^y(zx)=b
=>   b^(xyz)=b^1
Therefore,      xyz=1                     (Taking base as same)
SHANMUKESHWAR
461 Points
7 years ago
c^z=aa^x=b,
b^y=c(c^z)^x=b (b^y)^zx=b
b^xyz=b^1 so
xyz=1
Sani Chattopadhyay
26 Points
5 years ago
If a = b = c = 1 then what will you tell??????? You must think about this....This was a CAT question....So it can not be so trivial..

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