If 1,log9(31−x+2), log3(4.3x−1) are in A.P, then x is equal to

1,log9(31−x+2), log3(4.3x−1) are in A.P∴          2log9(31−x+2)=1+log3(4.3x−1)⇒          2log32(31−x+2)=log33+log3(4.3x−1)⇒          22log3(31−x+2)=log3(3{4.3x−1})⇒        31−x+2=3.(4.3x−1)⇒        3+2.3x=12.32x−3.3x⇒        12(3x)2−5(3x)−3=0∴               3x=3/4,  3x≠−1/3                    x=log34 3 =1−log34  .