A) 3
B) 2
C) 1
D) zero
Correct Answer: C
Solution :
\[{{\log }_{4}}(x-1)={{\log }_{2}}(x-3)\] \[\Rightarrow \]\[{{\log }_{{{2}^{2}}}}(x-1)={{\log }_{2}}(x-3)\] \[\Rightarrow \]\[\frac{1}{2}{{\log }_{2}}(x-1)={{\log }_{2}}(x-3)\] \[\Rightarrow \]\[(x-1)={{(x-3)}^{2}}\] \[\Rightarrow \]\[{{x}^{2}}-7x+10=0\] \[\Rightarrow \]\[(x-2)(x-5)=0\] \[\Rightarrow \]\[x=2,5\] But at\[x=2\]given equation is not satisfied. Hence, meaningful solution is 1.
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