Wednesday, November 7, 2007

Logarithm Laws

Hey its Anthony. Im the scribe...again. Ok today we started the morning class off with getting back all our old work and tests. My oh my was that a heartbreak, but then again it really was a wake up call to reality. So here I am, trying to do better. Back to topic we did our usual warm up questions and we got introduced to a new idea. Actually three new Laws. The Product Law, The Quotient Law, and the Power law.

Now here are some steps to use each of the following laws. We are going to start with the Product law since it the was the first that was introduced to us.

The product law. *When we use these laws we can look back to the log formula for reference.
The formula is as follows:

b = base
c = power
a = exponent

Example question *taken from todays slides*.

1)So we start by expanding. Then we get the first line.

2)Secondly As we know 2 is the base and 8 and 16 are the power. Now we ask our selves. "2 to the power of what equals 8 and 2 to the power of what equals 16". So we get 2 to the exponent 3 equals 8 and 2 to the exponent 4 equals 16. Right? check your calculator!

3)Now to refer back to our Product law, when adding 2 logs together we multiply the exponents. Now back to the question, we have now established 3 and 4 are the exponents and 2 is the base. Now the hard part 3 + 4 = ?

The second Law introduced to us was the Quotient Law.

Example question *taken from todays slides*

1)Ok again lets start with expanding to get the first line. Ok now we refer to the quotient Law. "When taking the difference of 2 logs we divide Log M by Log N."By doing this we M = 32 and N = 128. Since the Law is M/N. Now exspanding we get line 1.

2)Next we figure out the exponents and the base. To do that we refer bac
k to the Log formula. So now we are at the base is once again 2 and we ask ourselves the same question. "2 to the exponent of what equals 32 and 2 to the exponent of what equals 128." I believe 2 to the exponent of 5 equals 32 and 2 to the power of 7 equals 128. Check your calculators!

3)Now we have the exponents 5 and 7. Plug it into the Equation and Tada! The answer is negative 2.

Lastly The Power Law.

I found this law the most difficult to grasp. As Mr. K said. " This is what students get upset about, its so simple that its difficult"

Example question *taken from our slides today*.
1)Ok again lets start by Determining the base and exponents. So by looking at the question and refering to the Log formula the base is 2 again... and the power is 8. Lets asks ourselves "2 to the exponent what equals 8?" I believe it is 3. Check your calculators!

2)So now we have 2 to the exponent 3 IN BRACKETS to the exponent 5. So what is the rule when you have powers to the exponent of whatever? You multiply exponents. Ok back to the question. Remembering the rule we get 3 multiplied by 5. So we get an answer of 15. Sweet.


1 comment:

Anonymous said...

Well I must say hats off to you all. I haven't taken any Calculus for at least 7 years, but I do remember just how confusing it can be. You did a great job of explaining all the steps because I was able to follow everything.

Geoff G. (Mentor)
U of R