Question

Which expressions are equivalent to the one below? Check all that apply. log 3(81) + log 3(81)

Answer 1

Answer: We have to find the equivalent expressions, the simplification process leads to the following few results:

`\log_3(81)+\log_3(81)\rightarrow(1)`

Few properties used are:

`n\log_m(s)=\log_m(s^n)`

Simplification of (1):

`\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}`

Therefore the answers are (D) and (B).