Question

Write expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions.

Answer 1

Note: Laws Of Logarithm To Use

`\begin{gathered} (1).\text{ }log_a(M)-log_a(N)=log_a((M)/(N)) \\ \\ (2).\text{ }log_a(b^n)=nlog_a(b) \end{gathered}`

From the question, we have

`\begin{gathered} log_3(18)-log_3(2) \\ \\ log_3((18)/(2)) \\ \\ log_3(9)\text{ } \\ \\ The\text{ above expression is single logarithm} \end{gathered}`

To evaluate, we have

`\begin{gathered} log_3(9)=log_3(3^2) \\ \\ log_3(9)=2log_3(3) \\ \\ log_3(9)=2(1) \\ \\ log_3(9)=2 \end{gathered}`

The answer is

`2`