Elasticity from linear and log-log regression model

I am having problem understanding the calculation of elasticity. if I am using the log-log model eg: log(Y)=constant+β1 log(X1)+β2 log(X2) . So i would get the elasticity as β1 and β2 . If I am using the same data and find the linear model without using log for example Y=constant + β1X1+β2X2 , the formula for elasticity of X1 would be β1*(X1/Y). My problem is why I the elasticity of log-log differ form the linear model when they came from the same data?


Less is more. Stay pure. Stay poor.
Not completely my realm but what do the two models look like when you plot them and what do the residuals look like?
Its a multiple linear regression model. When I use log both on Y and X's variable, the coefficient should be the elasticity right? But if I am not using the log function, I need to use calculate the elasticity using the coefficient β times the average X over average Y. But although using the same data, both model give different elasticity. Are the average X divide the average Y not accurate for calculating elasticity?

And, yes I am still going through the text book mentioned.