Question

Prove that ` log_(10) 2" lies between " 1/4 and 1/3`.

Answer 1

We have to prove that`1/4 lt log_(10)2 lt 1/3`.
Consider ` log_(10) 2 gt 1/4`
` rArr 2 gt 10^(1/4)`
`rArr 2^(4) gt 10`, which is true
Now consider ` log_(10) 2 lt 1/3`
` rArr 2 lt 10^(1/3)`
` rArr 2^(3) lt 10 `, which is true.
Thus, ` 1/4 lt log_(10) 2 lt 1/3`