Find the value of x for the logarithmic function logx(4x - 3) = 2.
Solution
Correct Answer: Option D
logx(4x - 3) = 2
⇒ x² = 4x - 3
⇒ x² - 4x + 3 = 0
⇒ x² - 3x - x + 3 = 0
⇒ x(x - 3) - 1(x - 3) = 0
⇒ (x - 3)(x - 1) = 0
∴ x = 1, 3
⇒ x² = 4x - 3
⇒ x² - 4x + 3 = 0
⇒ x² - 3x - x + 3 = 0
⇒ x(x - 3) - 1(x - 3) = 0
⇒ (x - 3)(x - 1) = 0
∴ x = 1, 3
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