Question

is a power X equal to b b power Y equal to C C power Jet equal to a then xyz equal to​

Answer 1

Answer:

A^x= b^y = c^z , from this if we like to express A & c in terms of b —-

A^x = b^y, => A = b^(y/x) , similarly , as c^z = b^y Therefore , c = b^(y/z). It is also given that ——

b^2 = Ac,

or,b^2 = {b^(y/x)}*{b^(y/z)} ( putting the value of A & c defined in terms of b )

Or, b^2= b^(y/x+y/z)

or, b^2 = b^{( yz +xy)/xz }

or, (xy + yz)/xz =2 (as base on the both side equals (b) , power is equal)

or, xy + yz = 2xz

or, y(x+z) = 2xz

So, y = 2xz/(x+z)

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Answer 2

Answer:

givena^{x} = bax=b --(i)

givena^{x} = bax=b --(i)b^{y}=cby=c --(ii)

givena^{x} = bax=b --(i)b^{y}=cby=c --(ii)c^{z}=acz=a --(iii)

givena^{x} = bax=b --(i)b^{y}=cby=c --(ii)c^{z}=acz=a --(iii)use(iii)in(i)

givena^{x} = bax=b --(i)b^{y}=cby=c --(ii)c^{z}=acz=a --(iii)use(iii)in(i)c^{zx}=bczx=b ---(iv)

givena^{x} = bax=b --(i)b^{y}=cby=c --(ii)c^{z}=acz=a --(iii)use(iii)in(i)c^{zx}=bczx=b ---(iv)use(ii)in(iv)

givena^{x} = bax=b --(i)b^{y}=cby=c --(ii)c^{z}=acz=a --(iii)use(iii)in(i)c^{zx}=bczx=b ---(iv)use(ii)in(iv)b^{xyz} =bbxyz=b

givena^{x} = bax=b --(i)b^{y}=cby=c --(ii)c^{z}=acz=a --(iii)use(iii)in(i)c^{zx}=bczx=b ---(iv)use(ii)in(iv)b^{xyz} =bbxyz=bhere bases are equal hence powers are also equal

givena^{x} = bax=b --(i)b^{y}=cby=c --(ii)c^{z}=acz=a --(iii)use(iii)in(i)c^{zx}=bczx=b ---(iv)use(ii)in(iv)b^{xyz} =bbxyz=bhere bases are equal hence powers are also equalhence xyz=1

Step-by-step explanation: