The number of solutions for the equation log4⁡2x2+x+1−log2⁡(2x−1)=1, is

log4⁡2x2+x+1−log2⁡(2x−1)=1⇒loge⁡2x2+x+1loge⁡(4)−loge⁡(2x−1)loge⁡2=1⇒    loge⁡2x2+x+1(2x−1)2    =loge⁡4⇒    2x2+x+1=44x2−4x+1⇒    14x2−17x+3=0⇒    (14x−3)(x−1)=0⇒    x=314,x=1But x=314does not lie in the domain of functionHence, X = 1is the only solution.