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We havelog22, 12log22+2x2x, log25.2x+1 in A.P.1, 12log22+2x2x, log25.2x+1 in A.P. logaa=1If A,B,C are in A.P.we get2B=A+C2.12log22+2x2x=1+log25.2x+1log22+2x2x=1+log25.2x+1log22+2x2x-log25.2x+1=1log22+2x2x5.2x+1=1 loga-logb=logab2+2x2x5.2x+1=212+2x=2.2x5.2x+1Let 2x=t2+t=2t5t+110t2+2t-t-2=010t2+t-2=010t2+5t-4t-2=05t2t+1-22t+1=05t-22t+1=0t=25 or t=-122x=25 or 2x=-12But 2x cannot be negative.2x=25log22x=log225x.log22=log22-log25x=1-log25

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