Click here to purchase the entire book in PDF format. Logarithms Once upon a time you learned to do multiplication, after which someone explained that you can use division to do the reverse. For example: if $$A = B * C$$ (2.7) then $$\frac{A}{B} = C$$ (2.8) and $$\frac{A}{C} = B$$ (2.9) Logarithms sort of work in the same way, except that they are the backwards version of an exponent. (Just as division is the backwards version of multiplication.) Logarithms (or logs) work like this: If $10^{2} = 100$ then $\log_{10} 100 = 2$ Actually, it's: If $A^{B} = C$ then $\log_{A} C = B$ Now we have to go through some properties of logarithms. $\log_{10} 10 = 1$ or $\log_{10} 10^{1} = 1$ $\log_{10} 100 = 2$ or $\log_{10} 10^{2} = 2$ $\log_{10} 1000 = 3$ or $\log_{10} 10^{3} = 3$ This should come as no great surprise - you can check them on your calculator if you don't believe me. Now, let's play with these three equations. $\log_{10} 1000 = 3$ $\log_{10} 10^{3} = 3$ $3 * \log_{10} 10 = 3$ Therefore: $\log_{C} A ^{B} = B * \log_{C} A$