A) 5/2
B) \[{{\log }_{2}}5\]
C) \[{{\log }_{3}}5\]
D) 3/2
Correct Answer: B
Solution :
As, \[\log 2,\ \log ({{2}^{n}}-1)\] and \[\log ({{2}^{n}}+3)\] are in A.P. Therefore, \[2\log ({{2}^{n}}-1)=\log 2+\log ({{2}^{n}}+3)\] \[\Rightarrow ({{2}^{n}}-5)({{2}^{n}}+1)=0\] As \[{{2}^{n}}\] cannot be negative, hence \[{{2}^{n}}-5=0\] \[\Rightarrow {{2}^{n}}=5\] or\[n={{\log }_{2}}5\].
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