If log10⁡2,log10⁡2x−1 and log10⁡2x+3 are three consecutive terms of an A.P. for

2,2x−1,2x+3 are in G.P.⇒2x−12=22x+3⇒22x−22x+1=22x+6⇒22x−42x−5=0⇒2x−5(2x+1)=0⇒2x=5 ∵2x+1>0Thus, there is exactly one value of x.