Hey mates!!!
Need some help from u all...
Plz solve this question!
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6
Hey Mate !
Here is your solution :
Given,
=> a^x = b ----------- ( 1 )
=> b^y = c ----------- ( 2 )
=> c^z = a ------------ ( 3 )
Multiplying ( 1 ) , ( 2 ) and ( 3 ),
=> ( a^x ) × ( b^y ) × ( c^z ) = abc
On comparing ,
=> a^x = a^1
As bases are equal , so exponent will be also equal.
=> x = 1 --------- ( 4 )
And,
=> b^y = b^1
As bases are equal , so exponent will be also equal.
=> y = 1 --------- ( 5 )
Again,
=> c^z = c^1
As bases are equal , so exponent will be also equal.
=> z = 1 ----------- ( 6 )
Multiplying ( 4 ) , ( 5 ) and ( 6 ).
=> ( x ) ( y ) ( z ) = 1 × 1 × 1
=> xyz = 1
★ Proved ★
Another Method :
Given,
=> a^x = b
Let , b = k
=> a^x = b = k
=> a^x = k
=> a = k^( 1/x )
And,
=> b^y = c
=> b = c^( 1/y )
But , we have b = k
=> k = c^( 1/y )
=> k^y = c -------- ( 1 )
And,
=> c^z = a
=> c = a^( 1/z )
We have a = k^( 1/x )
=> c = [ k^( 1/x ) ]^( 1/z )
=> c = k^( 1/xz )
From ( 1 ),
=> k^y = k^( 1/xz )
As bases are equal,so exponent will be also equal.
=> y = 1/xz
=> xyz = 1
★ Proved ★
===============================
Hope it helps !! ^_^
Here is your solution :
Given,
=> a^x = b ----------- ( 1 )
=> b^y = c ----------- ( 2 )
=> c^z = a ------------ ( 3 )
Multiplying ( 1 ) , ( 2 ) and ( 3 ),
=> ( a^x ) × ( b^y ) × ( c^z ) = abc
On comparing ,
=> a^x = a^1
As bases are equal , so exponent will be also equal.
=> x = 1 --------- ( 4 )
And,
=> b^y = b^1
As bases are equal , so exponent will be also equal.
=> y = 1 --------- ( 5 )
Again,
=> c^z = c^1
As bases are equal , so exponent will be also equal.
=> z = 1 ----------- ( 6 )
Multiplying ( 4 ) , ( 5 ) and ( 6 ).
=> ( x ) ( y ) ( z ) = 1 × 1 × 1
=> xyz = 1
★ Proved ★
Another Method :
Given,
=> a^x = b
Let , b = k
=> a^x = b = k
=> a^x = k
=> a = k^( 1/x )
And,
=> b^y = c
=> b = c^( 1/y )
But , we have b = k
=> k = c^( 1/y )
=> k^y = c -------- ( 1 )
And,
=> c^z = a
=> c = a^( 1/z )
We have a = k^( 1/x )
=> c = [ k^( 1/x ) ]^( 1/z )
=> c = k^( 1/xz )
From ( 1 ),
=> k^y = k^( 1/xz )
As bases are equal,so exponent will be also equal.
=> y = 1/xz
=> xyz = 1
★ Proved ★
===============================
Hope it helps !! ^_^
Anonymous:
hehe
:)
:-)
How is yr day going
Superb
Urs
Good
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bye
Bye
Answered by
4
a=(b)^1/x
b=(c)^1/y
c=(a)^1/z
a={(c)^1/y}^1/x
PUTTED b= c^1/y VALUE
a=[{(a)^1/z}^1/y]^1/x
PUTTED c= (a)^1/z VALUE
(a)^1=(a)^1/xyz. BASE SAME
1=1/xyz
xyz=1
PROVED
:)
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