Please help, I'm getting options b and c both as the answer. 5 . If log 10 2 , log 10 2 x - 1 and log 10 2 x + 3 are three consecutive terms of an AP , then which one of the following is correct ? a x = 0 b x = 1 c x = log 2 5 d x = log 5 2 Share with your friends Share 0 Neha Sethi answered this Dear student Given: log102, log102x-1 and log102x+3 are in A.P⇒2 log102x-1= log102+ log102x+3⇒log102x-12= log102.2x+3⇒2x-12=2.2x+3⇒22x+1-2.2x=2.2x+6⇒22x+1-2.2x-2.2x-6=0⇒22x-4.2x-5=0⇒2x2-42x-5=0Let 2x=t⇒t2-4t-5=0⇒t2-5t+t-5=0⇒tt-5+1t-5=0⇒t+1t-5=0⇒t+1=0 or t-5=0⇒t=-1 or t=5So, t=2x=-1 and t=2x=5i.e. 2x=-1not possibleand 2x=5log2x=log5⇒xlog2=log5⇒x=log5log2x=log25Note:logmn=nlogmlogafx=logagx⇒fx=gxlogm+logn=logm.nWhen 3 terms a,b and c are in AP⇒2b=a+c logab=logbloga Regards 0 View Full Answer