SOLUTION: log (100,00xy) simplify

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: log (100,00xy) simplify      Log On


   



Question 624952: log (100,00xy) simplify
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Is that a 100 with a comma instead of a decimal? Or 100,000 with a missing zero? I'm going to guess the latter.

log(100000xy)
We can use a property of logarithms, log%28a%2C+%28p%2Aq%29%29+=+log%28a%2C+%28p%29%29+%2B+log%28a%2C+%28q%29%29, to split this logarithm. The reason we are splitting it is that 100,000 is a power of 10 and the base of log is 10. So we will be able to simplify log(100000):
log(100000) + log(xy)
Since 100000+=+10%5E5, log(100000) = 5. So now we have:
5 + log(xy)
This is as far as we can simplify this expression.