Your calculator might use Karatsuba or Toom–Cook algorithms or some hybrid.
The way I just solved the problem in my head was like this: 1) 314 X 1.5 (one and a half of 314) and I get 450 + 21 which is 471. But since it's 150 instead of 1.5, make that 47,100.
2) 314 X 9 = 314 X 3 X 3 = 942 X 3 = 2826.
3) 47,100 + 2826 = 49,926. Each one of those steps is fairly easy to do in your head -- a heck of lot easier than figuring out logarithms.