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(d) obtion is right
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As they are in AP their common difference will be same
so ㏒3(2∧x -5) - ㏒3(2) = log3(2∧x-7/2) - ㏒3(2∧x -5)
⇒ ㏒3{(2∧x -5)/2}=log3{(2∧x-7/2)/(2∧x -5)}
⇒(2∧x -5)/2=(2∧x-7/2)/(2∧x -5)
⇒(2∧x -5)²=2∧x × 2 - 7
let 2∧x be a
⇒ (a-5)²= (2a-7)
⇒a²-12a+32=0
⇒(a-4)(a-8)=0
∴2∧x=4 or 2∧x =8
so, x=2 or x=3
∴option (d) is correct
Anubhavdeb:
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