If 2^x =3^y=12^z, prove that x =2yz/y-z
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Let 2^x=3^y=12^z=r
Then
2=r^ 1/x,
3=r^1/y
and 12=r^1/z
Since 12=2^2⋅3,
r^1/z=r^2/x⋅r^1/y,
or
2/x=1/z−1/y = (y−z)/yz
Thus x=2yz / (y−z)
good evening_____________✌️✌️✌️✌️✌️
Let 2^x=3^y=12^z=r
Then
2=r^ 1/x,
3=r^1/y
and 12=r^1/z
Since 12=2^2⋅3,
r^1/z=r^2/x⋅r^1/y,
or
2/x=1/z−1/y = (y−z)/yz
Thus x=2yz / (y−z)
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