If $\log _{10} 2, \log _{10}\left(2^x+1\right)$ and $\log _{10}\left(2^x+3\right)$ are in A.P, then

Question

If $\log _{10} 2, \log _{10}\left(2^x+1\right)$ and $\log _{10}\left(2^x+3\right)$ are in A.P, then the value of $x$ is

Professor PC Thomas Classes · Answer

Solving the logarithmic progression gives $x = \log_2 5$.