Question

If 2^x= 3y=12^z,prove that x=2yz/y-z​

Answer 1

Step-by-step explanation:

solution Here,

given,

2^x = 3^y = 12^z = k(let)

then,

2^x=k

2 = k^1/x

3^y=k

3 = k^1/y

and 12^z=k

12 = k^1/z

or, 3×4 = k^1/z

or, k^1/y × 2 x 2 = k^1/z

or, k^1/y × k^1/x × k^1/x = k^1/z

or, k^1/y+1/x+1/x = k^1/z

or, k^1/y+2/x = k^1/z

or, 1/y+2/x = 1/z

or, x+2y/xy = 1/z

or, x+2y = 1/z ×xy

or, x+2y = xy/z

or, z(x+2y) = xy

or, zx + 2yz = xy

or, 2yz = xy-zx

or, 2yz = x(y-z)

or, x(y-z) = 2yz

or, x = 2yz/y-z

hence, x = 2yz/y-z. proved