So logarithms have some unique properties
when you're talking about the logarithm of
a product or of a quotient or of a number
with an exponent attached to it.
So, let's look at those properties.
First, let's look at the multiplication rule
for logarithms.
Here's the multiplication rule.
log base b of x times y where b can be any
base you like and then x times y, those are
just two numbers, you know their product shouldn't
be negative.
You don't want to plug a negative number into
a logarithm.
What we get is log base b of x plus log base
b of y. Alright so the log of a product is
equal to the sum of the logs of each of the
individual terms.
Fair enough.
What about the division rule?
Log of x divided by y is log of x minus log
of y.
Fair enough.
Now the last rule, the exponent rule.
Log base b of x to the y is y times log of
x.
So that means that if you have a number to
an exponent and you are taking the logarithm
of that, you can bring the exponent down out
in front.
It's pretty neat.
Alright so lets condense and expand some logarithmic
expressions using these rules.
