Question

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

Answer 1

Answer:

Option C.

Step-by-step explanation:

Note: It is given question and option "=" sing is missing. On some places it should be "=" instead of "=".

Consider the given equation is

$\log_2(x+11)=4$

Using properties of \logarithm we get

$(x+11)=2^4$             $[\because \log_ax=b\Leftightarrow x=a^b]$

$x+11=16$

$x=16-11$

$x=5$

The solution is x=5.

To check the solution, substitute x=5 in the given equation.

$\log_2(5+11)=4$

$\log_2(16)=4$

$\log_22^4=4$

$4=4$

$LHS=RHS$

Therefore, x-5 is a true solution because $\log_2(16)=4$.