The number of meaningful solutions of log4(x – 1) = log2 (x – 3) is -Maths 9th

The number of meaningful solutions of log4(x – 1) = log2 (x – 3) is -Maths 9th
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(b) 1log4(x – 1) = log2(x – 3) ⇒ log22 (x − 1) = log2(x – 3)⇒ \(rac{1}{2}\) log2 (x–1) = log2 (x– 3) ⇒ log2 (x–1) = 2 log2 (x– 3)\(\big[\)Using logam (bn) = \(rac{n}{m}\) loga b\(\big]\)⇒ log2(x – 1) = log2(x – 3)2 ⇒ (x – 1) = (x – 3)2 ⇒ x – 1 = x2 – 6x + 9 ⇒ x2 – 7x + 10 = 0 ⇒ (x – 2) (x – 5) = 0 ⇒ x = 2 or 5 Neglecting x = 2 as log2(x – 3) is defined when x > 2.⇒ There is only one meaningful solution of the given equation.
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