So first of all, we're going to define three important rules of logs.
This you can apply to any log base, so be at log base e which is ln, or log base 10 which is just log,
or any other base. If I give you the rules firstly, rule number 1 is known as the addition rule,
so that states that if you have log base a of x plus log base a of y.
You can combine this into one log term which is just log base a, x times y.
So look at what we're doing if you have the same base number,
you can rewrite or you can add the two logs, by just multiplying these numbers in there.
So log base a of x, plus log base a of y, is the same as log base a of xy.
The second rule is the subtraction rule, so if you have log base a of x minus log base a of y,
this combines to the log base a of x over y.
So it actually divides because it's been subtracted.
Again, if you use the pH scale, you can just check if the bases are the same,
you are allowed to combine the logs into one logarithmic term.
The last rule is one of the most useful rules, when it comes to solving for exponentials,
and that is this if you have log base a of x to the power of n,
you are allowed to bring this n to the front.
So know where the mathematical function really allows you to do that,
so you can bring the power down and then actually use it to solve it.
So you can rewrite this as n log base a of x.
And these are the three rules of logs.
We will quickly look over the proofs of these rules,
and then we'll start to look at some questions involving ln's.