In our study of exponents,
we found properties
about these exponents.
Logarithms, which are inverses
of exponential functions,
have similar properties
that are rooted
in the properties of exponents.
We will transition our
properties about exponents
to properties about
logarithms using
that log base b of b to the x
is just x, and b to the log base
b of x is x as well.
The first property that
we found about exponents
was that if we have b to
the m times b to the n, then
this is b to the m plus n.
For logarithms, this translates
to log base b of x times y
is log base b of x
plus log base b of y.
If you'd like to
see a proof of this,
you can click the
link to the right.
Our second property about
exponents that we found
is that b to the m divided by b
to the n is b to the m minus n.
The analog property
for logarithms
is that log base b of
x over y is log base
b of x minus log base b of y.
Again, if you would like
to see the proof of this,
you can click the
link to the right.
Next, we had the
property about exponents
that b to the m then
raised to the n power
is b to the m times n.
This can be used to prove
the property about logs
that log base b of x to the
p is p times log base b of x.
And again, the proof of this
is in the link to the right.
It's worth pointing out
that the third property will
be most useful to us to try to
solve the equations involving
exponents that we
could not solve before.
