An expression for a dimensionless quantity $P$ is given by $P = \frac{\alpha}{\beta} \log_{e} \left( \frac{kt}{\beta x} \right)$,where $\alpha$ and $\beta$ are constants,$x$ is distance,$k$ is the Boltzmann constant,and $t$ is the temperature. Then the dimensions of $\alpha$ will be:

• A
  $[M^{0} L^{-1} T^{0}]$
• B
  $[ML^{0} T^{-2}]$
• C
  $[MLT^{-2}]$
• D
  $[ML^{2} T^{-2}]$