Question

Simplify the expression log5(250). (Note (log(10)/(log(5) ≈ 1.4.)

Answer 1

Given the following expression:

`log_5(250)`

We have given the following note:

`(log(10))/(log(5))=1.4`

We will use the following rules to find the value of the given expression:

`\begin{gathered} log_a(b)=(log(b))/(log(a)) \\ \\ log(m^n)=n*log(m) \end{gathered}`

So, we will simplify the expression as follows:

`\begin{gathered} log_5(250)=(log(250))/(log(5))=(log(5^2*10))/(log(5))=(2*log(5)+log(10))/(log(5)) \\ \\ =(2*log(5))/(log(5))+(log(10))/(log(5))=2+1.4=3.4 \end{gathered}`

So, the answer will be 3.4