If log2(5.2x+1), log4(21−x+1)and 1 are in A.P, then x is equal to

From the given condition, we must have          2log4(21−x+1)=log2(5.2x+1)+1⇒         2log4(21−x+1)log4=log2(5.2x+1)log2+1⇒         2log(21−x+1)log4=log(5.2x+1)log2+1⇒        log(21−x+1)=log[(5.2x+1)2]⇒         21−x+1=5.2x.2+2Now, put 2x=y, so that2y+1=10y+2⇒  10y2+y−2=0⇒ (5y−2)(2y+1)=0Which meansy=2/5  or  y=−1/2.  Since y=2xcannot be negative, we havey=2x=2/5=0.4  ie.,  x=log2(0.4). But 2x=2/5can also express in the formx=log(2/5)log2=1−log5log2.