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The number of solutions of the equation \log_{4}\left ( x-1 \right )=\log_{2}\left ( x-3 \right ) is _______.
Option: 1 0
Option: 2 1
Option: 3 2
Option: 4 3

Answers (1)

best_answer

\\\log _{4}(x-1)=\log _{2}(x-3) \\ \Rightarrow \frac{1}{2} \log _{2}(x-1)=\log _{2}(x-3) \\ \Rightarrow \log _{2}(x-1)^{1 / 2}=\log _{2}(x-3)

\\\Rightarrow \sqrt{x-1}=(x-3)\\ \Rightarrow x-1=x^{2}+9-6 x \\ \Rightarrow x^{2}-7 x+10=0 \\ \Rightarrow(x-2)(x-5)=0 \\ \Rightarrow x=2,5

but x cant be 2, because in

\log_2(x-3)\rightarrow x>3

So, there is only one solution

Posted by

himanshu.meshram

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