A logarithm is just a power, (but often in decimal form)
If 2^l = 8 = 2^3
the power l = 3, is also the logarithm
With the understanding that the bold number should be subscript,
it is written l = log2 (8) = 3 and it means
"The power we must raise base 2 to, to get 8 is 3"
In the example given, x = log5 (1)
so 5^x = 1
but 5^0 =1
so x = 0
Regards - Ian