In this video we're going to introduce a new type of function that we've never seen before,
but it's a rather simple function and that's a logarithm.
Here, we're going to look at how logarithms are related to exponents.
Probably the best way to define a logarithm is to say that a logarithm is the exponent.
The log will always equal some exponent and how this works, if you noticed, we've got b as a base here.
Where the exponent is x, gives us some answer a.
We can rewrite this as a log and the way it works is we write the word log to show that we've rewritten it,
and then as a subscript, we write the letter b, which is the base of the exponential.
Log base b then is of a, we take the base of the answer and it will always equal the exponent x.
We say a log is an exponent because a log will always equal the exponent.
Notice also the base of the log, log base b is the same base as the base in the problem.
What is inside the log is what the answer was from the exponential problem.
The most important thing you can do with a logarithm at this point is convert between a log and an exponent,
And then convert an exponent to a log.
If you can make that conversion quickly and comfortably,
logarithms will be a very easy concept to work with.
So let's try this, we've got m squared equals twenty five, we want to change it to a log.
We have to write the word log and then the base is the little number as a subscript.
The base of the log is the same as the base of the problem.
Log base m of the answer of twenty five equals the exponent
because the log always equals the exponent, which is two.
Notice again, the base of m is the base of the log.
The answer from the problem goes inside the log and the log always equals the exponent.
Log base m of twenty five equals two is another way to write the problem m squared equals twenty five.
We can also convert the other way, we can change log base x of sixty four equals two.
I'm going to make that a two, and we can this in  exponential form as well.
The base of the log x is the base of the exponent. The exponent is whatever the log equals.
The log is an exponent, the log equals the exponent.
So we have x squared equals and then the sixty four.
Again, we see the same patterns, the base of the exponential is the base of the log,
the log always equals the exponent and finally the answer from the log.
I'm sorry, the answer from the exponent is what is inside the log.
The more comfortable you are with converting between logs,
and exponents the easier this next lesson is going to be.
