SOLUTION: I'm doing homework and I wasn't able to get to class because I was out of town. I have the worksheet, it tells me to Use the CHANGE OF BASE formula to evaluate the following. L

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: I'm doing homework and I wasn't able to get to class because I was out of town. I have the worksheet, it tells me to Use the CHANGE OF BASE formula to evaluate the following. L      Log On


   

Question 597170: I'm doing homework and I wasn't able to get to class because I was out of town. I have the worksheet, it tells me to Use the CHANGE OF BASE formula to evaluate the following.
Log2 (10)=x
Log12 (1243)=x
Most of the problems are like this. I looked at examples online, but none of the examples are set up like this.
What I have been doing is just setting the problem up differently for example Log2 (10)=x would be 10=2^x and I'm really really confused. I need help. Please someone respond.
Thanks
Found 2 solutions by stanbon, AnlytcPhil:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Log2 (10)=x
Log12 (1243)=x
----
Change of base Formula: log(Base A)B = [log(base C)B] / [log(base C)A]
Note: The "C" can be any positive number.
---
Your Problems:
x = log(10)/log(2) = 1/0.3010 = 2.3219
---------------
x = log(1243)/log(2) = 10.2796
==================================
Cheers,
Stan H.

Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
The change of base formula is:

log%28B%2CU%29 = log%28U%29%2Flog%28B%29

or

log%28B%2CU%29 = ln%28U%29%2Fln%28B%29
 
Therefore

log%282%2C10%29= x = log%282%29%2Flog%2810%29 =.3010299957%2F1 = .3010299957   

or you can use:

log%282%2C10%29 = x = ln%282%29%2Fln%2810%29 =.6931471806%2F2.302585093 = .3010299957 = .3010299957  

------------------------
Log12 (1243)=x

log%2812%2C1243%29 = x = log%281243%29%2Flog%2812%29 =3.094471129%2F1.079181246 = 2.867424856   

or you can use:

log%2812%2C1243%29 = x = ln%281243%29%2Fln%2812%29 =7.125283092%2F2.48490665 = 2.867424856

-------------------

Notice that you may use either "log" (which is base 10) or "ln" (which is
base "e").  Both are on your calculator.  The numbers you divide will be
different but when you divide them you will always get the same answer either way.

Edwin