Question

Which of the following expressions is equivalent to the expression shown below?

Answer 1

`2log_2(15)-log_2(5)+log_2(3)=log_2(15^2)-log_2(5)+log_2(3)\\=\log_2{(225*3)/(5)}=\log_2{135}`

Answer 2

Option C.
`log_(2)135`

Explanation:

The given expression is
`2log_(2)15-log_(2)5+log_(2)3`

We have to simplify this expression

`2log_(2)15-log_(2)5+log_(2)3`

=
`log_(2)(15^(2))-log_(2)5+log_(2)3` [Since
`log(a^(n))=n(loga)`]

=
`log_(2)225-log_(2)5+log_(2)3`

=
`log_(2)(225)/(5)+log_(2)3` [Since
`log(a)/(b)=loga-logb`]

=
`log_(2)(225* 3)/(5)` [Since
`log(a* b)=loga+logb`]

=
`log_(2)135`

Therefore, Option C.
`log_(2)135` is the answer.