Number of real solution of the equation |x-3|^(3x^2-10x+3)=1

First take log with base of 10...then equation becomes in product as (3x^2-10x+3).log|x-3|=0....,,,,then if 3x^2-10x+3=0 so x=3,1/3 but on checking values of x when we put x=3 the indetermiant form appears so x=3 neglected then second case is log|x-3|=0 therefore by solving x=4,2 ….hence the equation has only 3 solutions as x=1/3,4,2....