SOLUTION: Simplify the expression ln(8/e^4)

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Simplify the expression ln(8/e^4)      Log On


   

Question 490264: Simplify the expression ln(8/e^4)
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
There are three basic properties of logarithms:
log%28p%2C%28a%2Ab%29%29+=+log%28p%2C+%28a%29%29+%2B+log%28p%2C+%28b%29%29
log%28p%2C%28a%2Fb%29%29+=+log%28p%2C+%28a%29%29+-+log%28p%2C+%28b%29%29
and
log%28p%2C%28a%5Eb%29%29+=+b%2Alog%28p%2C+%28a%29%29

ln%288%2Fe%5E4%29
Since the argument of you logarithm is a quotient (division), we can use the second property on your logarithm:
ln%288%29+-+ln%28e%5E4%29
Since the argument of the second logarithm is an exponential term, we can use the third property on it:
ln%288%29+-+4%2Aln%28e%29
And finally, since log%28a%2C+%28a%29%29+=+1 for ALL bases and since the base for ln is e, ln(e) = 1. So the expression simplifies to:
ln%288%29+-+4%2A1
or
ln%288%29+-+4