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

Dear student
Given: log102,  log102x-1 and  log102x+3  are in A.P2 log102x-1= log102+ log102x+3log102x-12= log102.2x+32x-12=2.2x+322x+1-2.2x=2.2x+622x+1-2.2x-2.2x-6=022x-4.2x-5=02x2-42x-5=0Let 2x=tt2-4t-5=0t2-5t+t-5=0tt-5+1t-5=0t+1t-5=0t+1=0 or t-5=0t=-1 or t=5So, t=2x=-1   and  t=2x=5i.e. 2x=-1not possibleand 2x=5log2x=log5xlog2=log5x=log5log2x=log25Note:logmn=nlogmlogafx=logagxfx=gxlogm+logn=logm.nWhen 3 terms  a,b and c are in AP2b=a+c
logab=logbloga
Regards

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