Ans: (C)
Hint \(: x+\log _{10}\left(1+2^{x}\right)=x \log _{10} 5+\log _{10} 6\)
$$
\begin{aligned}
&\log _{10}\left(10^{x}\right)+\log _{10}\left(1+2^{x}\right)=\log _{10} 5^{x}+\log _{10} 6 \\
&2^{x}\left(1+2^{x}\right)=6 \\
&y(1+y)=6 \Rightarrow y=2 \Rightarrow 2^{x}=2 \Rightarrow x=1
\end{aligned}
$$
