Question

if 2x=3y=12z , show that (x+2y)z=xy

Answer 1

The solution is provided in the attachment. PLEASE MARK AS BRAINLIEST

Answer 2

Answer:

Given : 2^{x} = 3{y} = 12^{z}

To show : (x+2y)z=xy

Let 2^{x} = 3^{y} = 12^{z} = k

2 = k^{1/x}     3 = k^{1/y)    12 = k^{1/z}

k^{1/z} = 12 = 2^{2}×3  = k{2/x}×k^{1/y}

k^{1/z} = k^{2/x+1/y}

$\frac{2}{x} +\frac{1}{y} = \frac{1}{z}$

Taking L.C.M and then cross multiplying

$\frac{1}{z}= \frac{2y+x}{xy}$

xy = (x+2y)z