Hello and welcome to Math 101 with Joey
Today we will learn how to evaluate Logarithms
Lets first begin with vocabulary
The first vocab. word is Logarithm
A logarithm is a quantity showing what power a number
should be raised, to get a given number
The second vocab word is B.A.E
B.A.E is base, answer, exponenet
Remember this acronym because it will be useful later on
Ok now lets start with a warm-up
We are given two to the power of three equals X
This is asking what do you get if you
multiply 2 by itself three times
Ok, so lets do this, two times  two times two is eight
X is equal to eight
Okay, how do you solve a logarithm?
Here are given two equations, but they are the same thing
The equation is asking, how many times do you need to multiply three by itself to get twenty seven
Lets try 3 to the power of two first, this is nine
This is incorrect
Ok now, lets do three to the power of three, which equals 27, which is the correct answer
You can now right the log equation as Log base 3, 27 equals 3
Ok, how do we even write a logarithmic expression?
Here we are given two to the power of X
equals 32
This problem is asking us how many times do we need to multiply 2 with itself to get 32
Ok, now lets slove this
2 to the power of two is four, this is incorrect
two to the power of three is eight which is also incorrect
two to the power of four is 16, which is incorrect as well
two to the power of five is 32, therefore our answer is five
Now lets write the Logarithm using B.A.E
B.A.E is base, answer, exponent
First write log, then the base which is two
now lets write the answer which is 32
then equal it all to X which is our exponent
This means that two to the power of five is equal to 32
Ok, lets practice, pause the video and
do the three problems given
okay
the first problem is log base six, 36 is equal to X
write it in B.A.E
this is asking how many times do you need to multiply six by itself to get thirty six
six to the power of two is equal to thirty six, therefore this is our answer
okay now to the second one
This is log base 5, 625 is equal to X
First write it in BAE
This is asking how many times do you need to multiply five with itself to get 625
five to the power of two is twenty five, which is incorrect
five to the power of three is one hundred and twenty five, which is incorrect
five to the power of four is six hundred and twenty five, which is correct
ok, now lets do log base 1000, 1 is equal to X
ok, now lets write this in BAE form
1000 to the power of x is equal to one
heres a hint, anything to the power of zero is equal to one expect zero
So our answer is then zero
So 1000 to the power of zero is equal to one
And thats it, it wasn't that hard right?
Thanks for watching, I hope evaluating logarithms makes more sense now! Goodbye!
