If $\log _{10} 2, \log _{10}\left(2^x-1\right), \log _{10}\left(2^x+3\right)$ are three consecutive terms of an AP, then which one of the following is correct?

• A

  $x=0$
• B

  $x=1$
• Correct answer
  C

  $x=\log _2 5$
• D

  $x=\log _5 2$

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