If x = y^a , y = z^b , z = x^c , find the value of abc.
Ifx=ya,y=zb,z=xc, find the value of abc. Select an option to attempt
Correct Answer: Option A
Explanation
Solvingx=ya,y=zb,z=xcfor abc:Substitute chain:x=ya=(zb)a=zabzab=(xc)ab=xabcBut we started withx=xabc, so:xabc=x1⇒abc=1(This holds forx=0,1)Verification: ifx=4,y=2,z=2:a=logyx=log24=2;b=logzy=log22=2;c=logxz=log42=1/4;abc=2×2×41=1✔Answer:abc=1(Option 1).