Today, as in Friday, we learned more about logarithms  and the properties used with them. The three we learned were

log(a^n)=nlog(a)                      log(2^6)=6log(2)

log(a)+log(b)=log(a X b) log(2)+log(3)=log(6)

log(a)-log(b)=log(a/b)            log(10)-log(5)=log(2)

We derived these using different examples like the ones shown above.

Then we talked about using theses properties in equasions like

log(x)-log2(x-3)=3  —>  log((x-1)(x-3)) —> 2^3=(x-1)(x-3) —> x=5

Lastly, we reviewed teh logs we already know and practiced using them to fill in a number line.

log(4) = log(2) + log(2) = .602

log(5)= log(10/2) = log(10) – log(2) = .699

log(6) = log(3*2) = log(3) + log(2) = .778

etc….

Thanks(:

Today in class we reviewed what we learned yesterday and added some new log equations that can help find answers easier. Also, we looked at figuring out logarithms for 4 – 10 using the equations.

The logarithm equations (?) that we now have are:

log(a^n) = n log(a)       ex. log(2^5) = 5 log(2)

log(a) + log(b) = log (a*b)     ex. log(10) + log(2) = log(20)

log(a) – log(b) = log (a/b)      ex. log(30) – log(5) = log(6)

You can use the powers 10 scale to figure out the following problems or solve them using the equations above as I have them shown below:

log(4) = log(2) + log(2) = .602

log(5)= log(10/2) = log(10) – log(2) = .699

log(6) = log(3*2) = log(3) + log(2) = .778

log(8) = log(4*2) = log(4) + log(2) = .903

log(9)= log(3*3) = log(3)  + log(3) = .954

You can also use the equations to figure out more complicated logarithms:

log(8/3) = log(8) – log(3) = log(4) + log(2) – log(3) = .426

Hope this helped! The next scribe will be Steph Q.

Today in class, we learned a lot of new information about logarithms.  For those of you that are still a little bit uneasy about it, I will try my best and explain it.

First, we finished up talking about number 2 on activity 2.4.    In the first parts of activity 2.4, we were looking at the relationship between the exponent and power number lines.  We replicatied these number lines on our papers so we could easily measure from point to point.  Our conclusions were:

• For everychange of 1 for exponent, there is a multiplication of 10 for the power.
• For every change of 2 for exponent, there is a mulitplication of 100 for the power.

Knowing this simple knowledge of those relationships allowed us to dig even deeper into the material.  Our next table dealt with finding the exponent values when there was a change of *2 in the power value.  For this we measured from 1 to 2 on our power line and the exponent line and compared the ratio.  1 to 2 on the power line meaured about 18 mm.  1 to 2 on the exponent line measured about 59 mm.  We then concluded the ratio was about .301.  This means that every time you multiply 2 on the power line, you add .301 on the exponent line.  I tried my best to show that visually below:

Reversearp gave us a few examples of applying logarithms.  For example:

log64

log64 = log(2^6)

= 6(.301)

We then got the equation log a^n= nloga

After that we discussed that logarithms really just boil down to measurements and ratios.

Number 3 of activity 2.4 consisted of a girl named Emily who claimed that you can multiply any two power-scale numbers just by adding their corresponding logarithms.  She is indeed correct.  We can use log values you know to find ones that are unknown.  For example:

log6

log3 + log 2 = log 6

.301 + .477= .778

Then our class broke through and we learned a lot about multiplying power number.  The key is knowing that you can multiply the numbers by adding the logarithms.  Like we learned in earlier math subjects when you multiply numbers (powers), you add the exponents.

2^3+2^6 = 2^9

An example would be:

10 * 100

= 10^1 * 10^2

= 10^3

corresponds to…

log 1 + log 2 = 3

It would be easier to understand this to look at the example in the animation.  Click on the light blue link below to view it.  I know i didn’t explain this very well but I hope I helped a little bit.  I also sure that i messed up somewhere so please tell me so I can change it.  Reversearp can explain it a lot better so go ask him.  Please comment if you would like something cleared up.

2010-02-09_0956

P.S. the next scribe starts with a J and ends with an ocelyn.

The past two days in class, we have been working on Activity 2.4 in our packets. Activity 2.4 discusses the power scale versus the the exponent scale. By adding one on the exponent scale, we see that it is equivalent to multiplying by ten on the power scale. So, on the exponent scale, the difference [0,1] makes the difference on the power scale: [1, 10]. This is because 10^0 is 1, and 10^1 is 10. By realizing this, we can also prove that adding 2 on the exponent scale is equivalent to multiplying by 100 on the power scale. Therefore, we can say that 10^0 is 1, and 10^2 is 100. The difference between the two is a multiplication factor of 100.

As we moved on through Activity 2.4 we measured the distance from 1-2 on the power scale is 18 mm and the distance 0-1 on the exponent scale is roughly 59 mm. We divide 18 by roughly 59 to get .301. This proves that each multiplication by 2 on the power scale is adding another .301 on the exponent scale. log(2)= .301 which also means that 10^.301=2 because log(x)=y and 10^y=x. This lesson lead us to discover that log(a)^n = (n)log(a). We discovered this because a student pointed out that in order to find the log of 2^5 we need to move .301, 5 times down the exponent scale, because the exponent is 5. log(2^5) =5log(2). The distance from zero on the exponent scale is the logarithm of whatever number you’re looking for. We then began to work on a problem proving that you can multiply two power numbers by adding their logarithms. We didn’t get very far on this concept but so far we have seen: power 10*100 (and the logarithm of 10 is 1, 100, 2) is 1000=10^3. Adding their logarithms gives you 3, and 10^3 is 1000.

That just about sums up what we’ve done in class for the past two days. I can’t remember who the 3 people left on the list are so the next scribe is To Be Determined