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

Question

Rinkoo Gupta · Answer

a x =b => x=log a b b y =c=> y=log b c c z =a=> z=log c a xyz=(log a b.log b c).log c a =log a c.log c a =log a a =1 Thanks & Regards Rinkoo Gupta AskIITians Faculty

Sher Mohammad · Answer

a^xyz =(a^x)^yz =b^yz =(b^y)^z =c^z =a by comparision xyz=1 proved Sher Mohammad faculty askiitians

pramod Gopinath · Answer

a^x=b b^y=c =>a^xy=c c^z=a =>a^xyz=a =>xyz=1

Swati Kohli · Answer

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 · Answer

c^z=a a^x=b, b^y=c (c^z)^x=b (b^y)^zx=b b^xyz=b^1 so xyz=1

Sani Chattopadhyay · Answer

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..

Thank you for registering.

Register Now and Win Upto 25% Scholorship for a Full Academic Year !

Enter Your Details

Registration done!

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

6 Answers

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

Other Related Questions on Magical Mathematics[Interesting Approach]

ASK QUESTION

Answer and earn gift vouchers

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Complete Self Study Package designed by Industry Leading Experts

Live 1-1 coding classes to unleash the Creator in your Child

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Register Now & Win Upto 25% Scholorship