Question

Which of the following is true regarding the solution to the logarithmic equation below? log Subscript 2 Baseline (x + 11) = 4. x + 11 = 2 Superscript 4. x + 11 = 16. x = 5. x = 5 is not a true solution because log Subscript 5 Baseline (16) not-equals 2 x = 5 is not a true solution because log Subscript 5 Baseline (16) not-equals 4 x = 5 is a true solution because log Subscript 2 Baseline (16) = 4 x = 5 is a true solution because log Subscript 4 Baseline (16) = 2

Answer 1

C on edge2021

Explanation:

Answer 2

Option C.

Explanation:

The given logarithmic equation is

`\log_2(x+11)=4`

It can be written as

`(x+11)=2^4`
`[\because log_ax=y\Leftrightarrow x=a^y]`

`x+11=16`

`x=5`

Now, to check whether
`x=5` is a true solution or not. Substitute
`x=5` in the LHS of given equation.

`LHS=\log_2(5+11)`

`LHS=\log_2(16)`

`LHS=\log_22^4`

`LHS=4`
`[\because log_aa^x=x]`

`LHS=RHS`

Hence,
`x=5` is a true solution because
`\log_2(16)=4`.

Therefore, the correct option is C.