Question

Show that log√7 + log√20 - log√14 = 1/2

Answer 1

Alright, lets get started.

`log √(7) + log √(20) - log√(14) = (1)/(2)`

We could write this square root as
`(1)/(2)`

`log7^{(1)/(2)} + log20^{(1)/(2)}- log14^{(1)/(2)}`

Using the property of
`logm^(n ) = n log (m)`

`(1)/(2)log 7 + (1)/(2) log 20 - (1)/(2) log14`

`(1)/(2)` is common in each term, so

`(1)/(2)(log7 + log 20 - log 14)`

Using property of
`log m + log n = log(mn)`

`(1)/(2)(log 140 - log 14)`

Using property of
`log m - log n = log(m)/(n)`

`(1)/(2)log(140)/(14)`

`image`

log 10 value is 1 , hence

`(1)/(2) * 1 = (1)/(2)` : Answer

Hope it will help :)