If the fourth term in the binomial expansion of x11+log10⁡x+x1126 is equal to 200, and x>1 then the value of x is

Given binomial is x11+log10⁡x+x1126Since, the fourth term in the given expansion is 200∴  6C3x11+log10⁡x32x1123=200⇒  20×x321+log10⁡x+14=200⇒  x321+log10⁡x+14=10⇒ 321+log10⁡x+14log10⁡x=1[applying log10 both sides]⇒  6+1+log10⁡xlog10⁡x=41+log10⁡x⇒  7+log10⁡xlog10⁡x=4+4log10⁡x⇒ t2+7t=4+4t  t2+3t−4=0⇒  t=1,−4=log10⁡x⇒x=10,10−4⇒ x>1 Since, , x=10