SOLUTION: 1-2logbase3(squarroot 3/9)

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: 1-2logbase3(squarroot 3/9)      Log On


   

Question 611081: 1-2logbase3(squarroot 3/9)
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
1-2log%283%2C+%28sqrt%283%29%2F9%29%29
This problem is quite simple once you see that the base of the logarithm is 3 and that the argument is made up of powers of 3. Using the facts tht a square root is the same as a power of 1/2 and that 9 is 3 squared we get:
1-2log%283%2C+%28%283%29%5E%281%2F2%29%2F3%5E2%29%29

Using the rules for exponents for division (i.e. subtract the exponents) we get:
1-2log%283%2C+%28%283%29%5E%28-3%2F2%29%29%29

Now we can use a property of logarithms, log%28a%2C+%28p%5Eq%29%29+=+q%2Alog%28a%2C+%28p%29%29, we can move the exponent out in front:
1-2%2A%28-3%2F2%29%2Alog%283%2C+%283%29%29
Since log%283%2C+%283%29%29+=+1 by definition this becomes:
1-2%2A%28-3%2F2%29%2A1
which simplifies as follows:
1+3
4
So 1-2log%283%2C+%28sqrt%283%29%2F9%29%29+=+4