Trying to fix the log questions I got wrong. I've already fixed some, but I can't grasp these two in any way.

1) "log(15)1"

I did:

log(15)1 = x

15^x = 1

x = 1 ------> I corrected this with 15^0 = 1 ---> x = 0. But I can't grasp/remember the rule of anything to the zero becomes one. Does zero replace x?

2) "10^3x = 55"

I did:

10^3x = 55^1

3x = 55

x = 18.333 ---> I attempted to correct this and came up with x = log(10)55/3. I still resulted with x = 18.333 and I don't understand why this was still marked wrong.

Thanks in advance.