log base 3of 6 + log base3 (3x + 1) = 2

since loga + logb = log ab, we have

log3 6(3x+1) = 2
6(3x+1) = 9
18x = 3
x = 1/6

so, how come, when I worked this out for you, assuming base 10, you didn't just follow the same steps, with a change of base?