GATE 2024 Question 51: Dummy variables and functional forms

The following table provides different statistical model specifications along with the elasticity of $y_t$ with respect to $x_t$. Which one of the following options is correct?

Row	Statistical Model	Elasticity
1	$y_t=\beta_1+\beta_2\dfrac1{x_t}+\varepsilon_t$	$-\dfrac{\beta_2}{x_t^2}$
2	$y_t=\beta_1-\beta_2\ln(x_t)+\varepsilon_t$	$-\dfrac{\beta_2}{x_t}$
3	$\ln(y_t)=\beta_1+\beta_2\ln(x_t)+\varepsilon_t$	$\beta_2$
4	$\ln(y_t)=\beta_1+\beta_2x_t+\varepsilon_t$	$\beta_2x_t$
5	$\ln(y_t)=\beta_1+\beta_2\ln(x_t)+\varepsilon_t$	$\beta_2\exp(x_t)$
6	$\ln(y_t)=\beta_1+\beta_2x_t+\varepsilon_t$	$\beta_2\dfrac1{\exp(x_t)}$