A) 5/2
B) log 25
C) log 23
D) logs 2
Correct Answer: B
Solution :
\[\log 2,\log ({{2}^{x}}-1),\log ({{2}^{x}}+3)\]are in A.P\[2,({{2}^{x}}-1),({{2}^{x}}+3)\]are in G.P Put \[{{2}^{x}}=t\] \[2,(t-1)(t+3)\]are in G.P \[{{(t-1)}^{2}}=2(t+3)\]\[\Rightarrow \]\[{{t}^{2}}+1-2t=2t+6\] \[{{t}^{2}}-4t-5=0\] \[\Rightarrow \]\[{{t}^{2}}-5t+t-5=0\] \[t(t-5)+1(t-5)=0\]\[\Rightarrow \]\[t=-1,5\] \[\Rightarrow \]\[t\ne -1\] \[{{2}^{x}}=5\]or \[x={{\log }_{2}}5\]You need to login to perform this action.
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