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

The correct option is B 1log_4(x 1)=log_2(x 2) ⇒log(x 1)/log4 = log(x 2)/log2 ⇒log(x 1)/2log2 = log(x 2)/log2 ⇒ 2log(x 2)=log(x 1)=(x 2)^2 =x 1 ⇒ x^2 4x+4=x 1 ...

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Byju's Answer

Standard XII

Mathematics

Quadratic Formula for Finding Roots

The number of...

Question

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

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Solution

The correct option is B 1
$l o g_{4} (x - 1) = l o g_{2} (x - 2)$
$\Rightarrow \frac{l o g (x - 1)}{l o g 4} = \frac{l o g (x - 2)}{l o g 2}$
$\Rightarrow \frac{l o g (x - 1)}{2 l o g 2} = \frac{l o g (x - 2)}{l o g 2}$
$\Rightarrow 2 l o g (x - 2) = l o g (x - 1) = (x - 2)^{2} = x - 1$
$\Rightarrow x^{2} - 4 x + 4 = x - 1 \Rightarrow x^{2} - 5 x + 5 = 0,$
Which gives two solutions out of which only one is valid as only one solution satisfies the given equation.

Suggest Corrections

The number of solutions of : log4(x−1)=log2(x−2) is

The correct option is B 1log4(x−1)=log2(x−2) ⇒log(x−1)log4=log(x−2)log2 ⇒log(x−1)2log2=log(x−2)log2 ⇒2log(x−2)=log(x−1)=(x−2)2=x−1 ⇒x2−4x+4=x−1⇒x2−5x+5=0, Which gives two solutions out of which only one is valid as only one solution satisfies the given equation.

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