1 + 1 = 2 and 1 + 2 = 3

Log in the base 10 of 100 is 2 -- this is the only log ya gotta know ;)  this is because 10 to the 2 power is 100
Then the log rules (that make no sense because they work off of exponent rules) follow.

log 10 + log 10 = log 100
1 + 1 = 2

log 10 + log 100 = log 1000
1 + 2 =3

It makes people laugh when they see that:

1 + 1 = 2 and

1 + 2 =3!! ;)

The Main Thing About Logs -- Use Examples Not Formulas!!

Logarithms, like most topics in Math, are best learned and taught by example rather than formula. The log rules work like exponent rules so be wicked careful!!

If students know that log10100 = 2, they can see that 10^2 = 100. They can then apply this knowledge to any other log problem that comes up. Log 'rules' do not make sense!!
Just use thinking and analysis to remember the rules:

log101000 = 3
log10100 = 2
log1010 = 1

This is because logs are related to exponents!!

log10 (10^3) = 3

and

log10(10^2) = 2

and

log10(10^1) = 1

Therefore log 1000 = log 100 + log 10
(here you can build and see that 100*10 = 1000 and that their logs are related additively rather than multiplicatively)