Find the value of $x$ if $\log_3(x^2 - 2x) = 1$.
Ax = 3 or x = −1CORRECT
Bx = −3 or x = 1
Cx = 3 or x = 1
Dx = −3 or x = −1
GCEFurther MathematicsSurds, Indices and Logarithms2023
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Why the answer is A, and why the others tempt you.
log₃(x² − 2x) = 1 means x² − 2x = 3¹ = 3. Rearranging: x² − 2x − 3 = 0, which factors as (x − 3)(x + 1) = 0, giving x = 3 or x = −1. Both values make x² − 2x = 3 > 0, so both are valid solutions.
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