Question

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

\\(\log_{2}(x+11) = 4\\)

\\(x+11 = 2^{4}\\)

\\(x+11 = 16\\)

\\(x = 5\\)

• \\(x = 5\\) is not a true solution because \\(\log_{5}(16) \

eq 2\\)

• \\(x = 5\\) is not a true solution because \\(\log_{5}(16) \

eq 4\\)

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

Explanation:

Solve the logarithmic equation

$$
LATEXBLOCK0
$$

Verify the solution

$$
LATEXBLOCK1
$$

Match with the given options

$$
LATEXBLOCK2
$$

Answer:

• (A) \(x = 5\) is not a true solution because \(\log_5(16)

eq 2\)

• (B) \(x = 5\) is not a true solution because \(\log_5(16)

eq 4\)

• (C) \(x = 5\) is a true solution because \(\log_2(16) = 4\) (Correct answer)
• (D) \(x = 5\) is a true solution because \(\log_4(16) = 2\)