Question

2^x=3^y=6^z,then 1/x+1/y+1/z​

Answer 1

Answer

${2}^{x} = {3}^{y} = {6}^{-z} = k$

Thus:

$2 = {k}^{ \frac{1}{x} } \\ 3 = {k}^{ \frac{1}{y} } \\ 6 = {k}^{ \frac{1}{-z} }$

We know that: 6 = 2 × 3;

${k}^{ \frac{1}{x} } \times {k}^{ \frac{1}{y} } = {k}^{ \frac{1}{-z} }$

Powers only:-

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

$\frac{1}{x} + \frac{1}{y} + \frac{1}{z} = 0$