Question

Which of the following is true regarding the solution to the logarithmic equation below?

Answer 1

c

Explanation:

Answer 2

Option C. is the correct option.

Explanation:

The given expression is
`log_(2)(x+11)=4`

We further solve this

`(x+11)=2^(4)=16`

`x = 16-11=5`

Now we evaluate the options

A).
`log_(5)16\\eq 2`

But the expression is given as
`log_(2)(x+11)=4`

Wrong expression so not correct.

B).
`log_(5)16\\eq 4`

Wrong expression again so not correct

C). By putting x = 5 in the expression

`log_(2)(x+11)=4`

`log_(2)(5+11)=log_(2)(16)=log_(2)(2^(4))=4`

Therefore this option is the correct option.

D). By putting x = 5 in the expression

`log_(4)(5+11)=log_(4)(16)=log_(4)(4^(2))=2`

But the expression is
`log_(2)(x+11)=4`

So this option is also not correct.