A book is worth $7.00 today, and its value grows at a rate of 9% per year. How long until the comic is worth $20?

Every year that you own this comic book, it will appreciate 9%. So, you will multiply the initial amount by 1.09 every year. This works out to a fairly straightforward equation.
Assuming Y is the resulting value (after appreciation), x is the number of years, A is the initial value, and r is the interest rate, this is the general equation.

Y = A*(1 + r)^x

In this case, the equation becomes the following:

20 = 7*(1.09)^x

Divide by 7 to simplify the equation prior to taking a logarithm. It doesn’t matter what base logarithm you use, as long as you do the same on both sides. To simplify, we’ll use log base 10, because it’s standard.
Log(20/7) = log(1.09^x)
The rule of logarithms with exponents is that the exponent becomes a multiplier for the logarithm. Therefore, you can isolate x like so:

Log(20/7) = x*log(1.09)

Divide each side by log(1.09) and you will have a result: 12.182 years.