Question

Consider the function f(x)= log5 xComplete the following and then graphx= 1/5 f(x)?x=1 f(x)? x=5 f(x)?x=25 f(x)?

Answer 1

Given:

`f(x)=\log_5x`

Required: Function values at x = 1/5, 1, 5, and 25.

Step-by-step explanation:

Use the logarithmic properties

`\log_b1=0,\log_b(A)/(B)=\log_bA-\log_bB,\log_bb=1,\log_bb^n=n`

To find f(1/5), substitute 1/5 for x into f(x).

`\begin{gathered} f((1)/(5))=\log_5((1)/(5)) \\ =\log_51-\log_55 \\ =0-1 \\ =-1 \end{gathered}`

To find f(1), substitute 1 for x into f(x).

`\begin{gathered} f(1)=\log_51 \\ =0 \end{gathered}`

To find f(5), substitute 5 for x into f(x).

`\begin{gathered} f(5)=\log_55 \\ =1 \end{gathered}`

To find f(25), substitute 25 for x into f(x).

`\begin{gathered} f(25)=\log_525 \\ =\log_55^2 \\ =2\log_55 \\ =2 \end{gathered}`