How do you simplify #10^(log_10 (19))#?
It may help to think of it like this:
I don't know the number that is the log base 10 of 19, but I can describe it.
The log base 10 of 19 is the power (exponent) I would need on the 10 (the base), to get 19.
Now I am asked to raise 10 to that power.
The power I'd need to put on 10 to get 19!
OK, then I'll get 19.
It's really a self-answering question.
(Like, "What color paint should I buy, if I want to paint my house blue?")
Here's another example:
This time I do know the log base 10 of the number. it is 2.
Because 2 is the power I need on 10, to get 100.
OK, now raise 10 to that power, and what do you get?