The number of solutions of log 4x-1-log 2x-3 isA- 1B- 2C- 3D- 0

The correct option is A 1Given, log_4(x 1)=log_2(x 3)=log_4^1/2 (x 3) ⇒ log_4(x 1)=log_4(x 3)^2 ⇒ (x 3)^2=x 1 ⇒ x^2+9 6x=x 1 ⇒ x^2 7x+10 =0 ⇒ (x 2)(x 5)=0 ⇒ x= ...

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Standard XIII

Mathematics

Roots of a Quadratic Equation

The number of...

Question

The number of solutions of $l o g_{4} (x - 1) = l o g_{2} (x - 3)$ is

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Solution

The correct option is B 1
Given, $l o g_{4} (x - 1) = l o g_{2} (x - 3) = l o g_{4^{\frac{1}{2}}} (x - 3)$
$\Rightarrow l o g_{4} (x - 1) = l o g_{4} (x - 3)^{2} \Rightarrow (x - 3)^{2} = x - 1 \Rightarrow x^{2} + 9 - 6 x = x - 1 \Rightarrow x^{2} - 7 x + 10 = 0$
$\Rightarrow (x - 2) (x - 5) = 0 \Rightarrow x = 2, o r x = 5$
$\Rightarrow x = 5 [∵ x = 2$ makes log (x-3)undfined].
Hence, one solution exists.

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The number of solutions of log4(x−1)=log2(x−3) is

The correct option is B 1Given, log4(x−1)=log2(x−3)=log412(x−3) ⇒log4(x−1)=log4(x−3)2⇒(x−3)2=x−1⇒x2+9−6x=x−1⇒x2−7x+10=0 ⇒(x−2)(x−5)=0⇒x=2,orx=5 ⇒x=5[∵x=2 makes log (x-3)undfined]. Hence, one solution exists.

The number of solutions of $l o g_{4} (x - 1) = l o g_{2} (x - 3)$ is