Alright, so now that we know a little bit
about how logarithms operate, let's talk about
some of the basic properties of logs.
So, for example, log base b of b equals one.
B could be anything so, log base two of two
log base three of three.
And, this should make some sense because you
raise b to the first power to get b.
You should always be thinking, what power
do I need to raise this to, there's your power,
to get that.
So let's continue with this.
Also, very similar, log base b of one is equal
to zero.
And that should make sense as well because
we need to raise b to the zero power to get
one.
So, log base two of one is zero.
So log base three of one is zero.
Log base eight of one is zero.
You get the idea.
Alright, lets go on to our next one.
Now this one's a little bit stranger.
B to the power of log base b of x equals x.
Why is that true?
This is a little bit difficult for people
unfamiliar with logarithms to understand at
first but if you think about it a little bit,
you'll get it.
So remember, log base b of x is the number
that you need to raise b to to get x.
So let's say that again, log base b of x is
the number you need to raise b to, to get
x.
So think about it.
Not so bad right?
Alright, let's see one more.
Log base b of b to the n equals n.
Again, just walk yourself through the words.
What power do I need to raise b to, to get
b to the n.
So you would need to raise b to the nth power
to get b to the n.
And there you go.
