JAMB UTME WAEC WASSCE NECO SSCE

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Mathematics Physics Chemistry English Lit

Explain log₂(x) + log₂(x-2) = 3. Solve for x. (JAMB UTME Algebra Prep)

Excellent Algebra query! Let's solve it together step-by-step:

  1. Apply Log Multiply Rule:
    log₂[x(x-2)] = 3
  2. Exponents Conversion:
    x(x-2) = 2³ ⇒ x² - 2x = 8
  3. Form Quadratic:
    x² - 2x - 8 = 0 ⇒ (x-4)(x+2) = 0

Since negative inputs are invalid for logarithms, we confirm x = 4.

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