log4(x−1)=log2(x−3) (given) ⇒log22(x−1)=log2(x−3) Using property of logarithm, logbca=
1
c
logba ⇒
1
2
log2(x−1)=log2(x−3) ⇒log2(x−1)=2log2(x−3) ⇒log2(x−1)=log2(x−3)2 On comparing, x−1=(x−3)2 or x−1=x2+9−6x ⇒x2−7x+10=0 ⇒x2−5x−2x+10=0 ⇒(x−5)(x−2)=0 ⇒x=2,5 x=2( rejected) as x>1 ∴x=5 is only solution i.e. number of solution is 1.