Question

please prove it
(full steps required)
(No spam answers)​

Answer 1

Answer:

Step-by-step explanation:

It's given in the question,

$2^x=3^y=12^z$

$2^x=12^z$

$\text{log}2^x}=\text{log}12^z}$

$x\text{log2}=z\text{log12}$

$x=\frac{z\text{log}12}{\text{log2}}$

$3^y=12^z$

$\text{log}3^y}=\text{log}12^z}$

$y\text{log}3}=z\text{log}12}$

$y=\frac{z\text{log12}}{\text{log}3}$

Now substitute the values in the equation,

$\frac{1}{y}+\frac{2}{y} =\frac{1}{\frac{z\text{log12}}{\text{log}3}}+\frac{2}{\frac{z\text{log}12}{\text{log2}}}$

         $=\frac{\text{log}3}{z\text{log}12}+\frac{2\text{log}2}{z\text{log}12}$                    

         $=\frac{\text{log}3+\text{log}2^2}{z\text{log}12}$

         $=\frac{\text{log}(3\times 2^2)}{z\text{log}12}$

         $=\frac{\text{log}(12)}{z\text{log}12}$

         $=\frac{1}{z}$

Hence proved.