which of the following is true regarding the solution to the logarithmic equation below?\nlog₂(x + 11)=4\nx…

which of the following is true regarding the solution to the logarithmic equation below?\nlog₂(x + 11)=4\nx + 11 = 2⁴\nx + 11 = 16\nx = 5\no x = 5 is not a true solution because log₅(16)≠2\no x = 5 is not a true solution because log₅(16)≠4\no x = 5 is a true solution because log₂(16)=4\no x = 5 is a true solution because log₄(16)=2

which of the following is true regarding the solution to the logarithmic equation below?\nlog₂(x + 11)=4\nx + 11 = 2⁴\nx + 11 = 16\nx = 5\no x = 5 is not a true solution because log₅(16)≠2\no x = 5 is not a true solution because log₅(16)≠4\no x = 5 is a true solution because log₂(16)=4\no x = 5 is a true solution because log₄(16)=2

Answer

Explanation:

Step1: Recall log - exponent conversion

The logarithmic equation $\log_{a}b = c$ is equivalent to $b=a^{c}$. Given $\log_{2}(x + 11)=4$, we convert it to $x + 11=2^{4}$.

Step2: Solve for x

Since $2^{4}=16$, the equation $x + 11=16$ gives $x=16 - 11=5$.

Step3: Check the solution

Substitute $x = 5$ into the original logarithmic equation. The left - hand side is $\log_{2}(5 + 11)=\log_{2}(16)$. And since $2^{4}=16$, $\log_{2}(16)=4$, which is equal to the right - hand side of the original equation.

Answer:

$x = 5$ is a true solution because $\log_{2}(16)=4$