Question

Which expressions are equivalent to the one below? Check all that apply.log3 3+ log3 27A. log3 81B. log3 (3^4)C. 4D. log 10

Answer 1

The given expression is

`log_33+log_327`

We will use the rule

`log_ba+log_bc=log_b(ac)`
`\begin{gathered} log_33+log_327=log_3(3*27) \\ \\ log_3(3*27)=log_3(81) \end{gathered}`

Since 81 = 3 x 3 x 3 x 3, then

`\begin{gathered} 81=3^4 \\ log_3(81)=log_3(3^4) \end{gathered}`

We will use the rule

`log_b(a^n)=nlog_b(a)`