Question

How do you simplify `10^(log_10 (19))`?

Answer 1

`10^(log_10 (19)) = 19`

Explanation:

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.

What 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:

`10^(log_10 100)`.

This time I do know the log base 10 of the number. it is 2.
Why?
Because 2 is the power I need on 10, to get 100.
OK, now raise 10 to that power, and what do you get?
`100`