Follow the line of reasoning in these various steps one by one with the captions listed below the equations.

1. Let's start with log 2 = 0.3 I have added perhaps more specification than needed by noting that the log is to base 10, but you will see how it comes into play.
2. If I told you that the log base 10 of something was 0.3, you'd tell me that that something was "2". Working it backwards is the "antilog."
3. Now let's take the wood - I mean - logs out of equation. So you see that the 0.3 power of 10 equals 2. Ah, ha! Draw circles around the similar portions of lines (b) and (c).
4. Here, for fun, I decided to take the log of both sides of (c)
5. I am allowed to move the exponent of 10 out in front to become a multiplier.
6. You know that the log base 10 of 10 is 1
7. And the equation becomes 0.3 = log 2, which is the same as (a)

Do these gymnastics make sense?