Question

Prove that ` 1/3 lt log_(20) 3 lt 1/2`.

Answer 1

`x= log_(20) 3`
` rArr 1/x = log_(3) 20`
We know that ` 3^(2) lt 20 lt 3^(3)`
` rArr 2 lt log_(3) 20 lt 3`
` rArr 2 lt 1/x lt 3`
` rArr x in (1/3,1/2)`