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