To solve this equation, we will first isolate the logarithm term by dividing by 1/3:

x^2 - 10x + 10 = 0

Now we can proceed to solve the quadratic equation using the quadratic formula:

x = [10 ± sqrt((-10)^2 - 4(1)(10))] / 2(1)

x = [10 ± sqrt(100 - 40)] / 2

x = [10 ± sqrt(60)] / 2

x = [10 ± 2sqrt(15)] / 2

x = 5 ± sqrt(15)

Therefore, the solutions to the equation Log1/3(x^2-10x+10)=0 are:

x = 5 + sqrt(15)
x = 5 - sqrt(15)