📢 Too many exams? Don’t know which one suits you best? Book Your Free Expert 👉 call Now!

    Question

    If log₂(x) + log₂(x − 2) = 3 and x is real, find

    x.
    A 2 Correct Answer Incorrect Answer
    B 4 Correct Answer Incorrect Answer
    C -2 Correct Answer Incorrect Answer
    D 8 Correct Answer Incorrect Answer

    Solution

    ATQ, Use log rule: log₂(x) + log₂(x − 2) = log₂[x(x − 2)]. So log₂[x(x − 2)] = 3 => x(x − 2) = 2³ = 8 => x² − 2x − 8 = 0 => x = [2 ± √(4 + 32)] / 2 = [2 ± √36]/2 = (2 ± 6)/2 => x = 4 or x = −2. Domain: For both logs to be defined, need x > 0 and x − 2 > 0 ⇒ x > 2. So only x = 4 is valid.

    Practice Next
    More Quant Miscellaneous Questions
    ask-question