$$ f(x)= \begin{cases}(1+3 x)^{\frac{4}{x},} & \text { if } x \neq 0, \\ a, & \text { if } x=0 .\end{cases} $$ If $f$ is continuous, then $\log a=$

• A

  $\frac{1}{3}$
• B

  $\frac{3}{4}$
• C

  $\frac{4}{3}$
• Correct answer
  D

  12

Hence, the correct answer is option: 'D'.