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

Answer:

Option C.

Step-by-step 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.