Question

Log (w2+21) - log (10)

Answer 1

`w =7\ or\ w =3`

Explanation:

Given

The right question is:

`\log(w^2+ 21) = \log(10w)`

Required

Solve for w

`\log(w^2+ 21) = \log(10w)`

Cancel log on both sides

`w^2+ 21 = 10w`

Equate to 0

`w^2 - 10w+ 21 = 0`

Split

`w^2 - 3w - 7w+ 21 = 0`

Factorize

`w(w - 3) - 7(w-3) = 0`

Factor out w - 3

`(w - 7)(w-3) = 0`

Solve for w

`w - 7 = 0\ and\ w - 3 = 0`

`w =7\ or\ w =3`