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If a^x=b b^y=c c^z=a Prove xyz=1 Please give the solution
ax=b => x=logab by=c=> y=logbc cz=a=> z=logca xyz=(logab.logbc).logca =logac.logca =logaa =1Thanks & RegardsRinkoo GuptaAskIITians Faculty
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
a^xyz=(a^x)^yz=b^yz=(b^y)^z=c^z=aby comparision xyz=1 provedSher Mohammadfaculty askiitians
a^x=bb^y=c =>a^xy=cc^z=a =>a^xyz=a =>xyz=1
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^1Therefore, xyz=1 (Taking base as same)
c^z=aa^x=b,b^y=c(c^z)^x=b (b^y)^zx=bb^xyz=b^1 soxyz=1
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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