Question

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

Answer 1

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,

`(1)/(y)+(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* 2^2)}{z\text{log}12}`

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

`=(1)/(z)`

Hence proved.