The correct option is C 1
Given: log3(−3x2+6x)=1
Now, for logarithm to be defined:
−3x2+6x>0⇒x2−2x<0⇒x(x−2)<0⇒x∈(0,2)⋯(A)
Now, log3(−3x2+6x)=1
⇒−3x2+6x=3⇒x2−2x+1=0⇒x=1⋯(B)
Now, x=1∈A∩B
Thus, x=1 is the only solution.
Hence the correct answer is option (b).