Answer: We have to find the equivalent expressions, the simplification process leads to the following few results:
[tex]\log_3(81)+\log_3(81)\rightarrow(1)[/tex]
Few properties used are:
[tex]n\log_m(s)=\log_m(s^n)[/tex]
Simplification of (1):
[tex]\begin{gathered} \log_3(81)+\log_3(81)=2\log_3(81) \\ \\ \\ \\ 2\log_3(81)=\log_3(81^2) \\ \\ \\ \\ \log_3(81^2)=\log_3((9^2)^2)=\log_3(9^4) \\ \\ \\ \\ \log_3(9^4)=\log_3((3^2)^4)=\log_3(3^8)\rightarrow(D) \\ \\ \\ \\ \log_3(3^8)=8\log_3(3)=8\rightarrow(B) \end{gathered}[/tex]
Therefore the answers are (D) and (B).
