Question

Match the three graphs to the function they represent ?

Answer 1

Suppose that a>b>1, then

`a^x>b^x` and
`\log_ax<\log_bx.`

Therefore, since 2<3<7,
`\log_2x>\log_3x>\log_7x.`

Choose an arbitrary x>1. You have that a takes the greatest values at x, c takes the smallest value at x. Thus,

a>b>c and

• 
  `a=\log_2x;`
• 
  `b=\log_3x;`
• 
  `c=\log_7x.`

Answer: correct option is B.