Question

pls help me with this doubt​

Answer 1

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

$2 = {k}^{ \frac{1}{x} } \\ 3 = {k}^{ \frac{1}{y} } \\ 12 = {k}^{ \frac{1}{z} }$

We know,

$4 \times 3 = 12$

$( {k}^{ \frac{1}{x} } )^{2} \times {k}^{ \frac{1}{y} } = {k}^{ \frac{1}{z} }$

${k}^{ \frac{2}{x} } \times {k}^{ \frac{1}{y} } = {k}^{ \frac{1}{z} }$

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

Since, the bases are same, so powers must be equal because equality holds here.

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

Hence, Proved