Number of real roots of the equation 2x+2x−1+2x−2=7x+7x−1+7x−2  is

Given equation is 2x+2x−1+2x−2=7x+7x−1+7x−2    ….. ( 1 ) ⇒2x+2x.2−1+2x.2−2=7x+7x.7−1+7x.7−2 ⇒2x(1+12+14)=7x(1+17+149) ⇒2x(74)=7x(5749) ⇒  74×  4957  =  (72)x   ⇒  243228  =  (72)x Applying log on both sides, we get⇒  xlog(72)=log(243228) ⇒  x=log(243228)log(72). ∴   Eq.( 1 ) has only one solution.