Question

answer the above question with clear steps

Answer 1

Hey Mate !!

Here is your solution :

Given,

a^x = b^y = c^z = d^w

Let,

a^x = b^y = c^z = d^w = k.

Now,

a^x = k

a = k^( 1/x ).

-------------------

b^y = k

b = k^( 1/y ).

--------------------

c^z = k

c = k^( 1/z )

----------------------

d^w = k

d = k^( 1/w ).

Given,

ab = cd

By substituting the values of a,b,c and d.

{ k^( 1/x ) × k^( 1/y ) } = { k^( 1/z ) × k^( 1/w ) }

Using,

{ a^m × a^n = a^( m + n ) }

k^{ ( 1/x ) + ( 1/y ) } = k^{ ( 1/z ) + ( 1/w ) }

As bases are equal,so exponent must be equal.

( 1/x ) + ( 1/y ) = ( 1/z ) + ( 1/w )

( y + x ) / xy = ( w + z ) / zw

( x + y ) / xy = ( z + w ) / zw

Proved !!

Hope it helps !!