SOLUTION: Hello, i just need a little help on a logarithmic problem. I am unawre of the difference between ln and log. the problem is: ln 5+(1/2)ln y-3ln(z+1) and the problem says 'rewr

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Hello, i just need a little help on a logarithmic problem. I am unawre of the difference between ln and log. the problem is: ln 5+(1/2)ln y-3ln(z+1) and the problem says 'rewr      Log On


   

Question 607675: Hello, i just need a little help on a logarithmic problem. I am unawre of the difference between ln and log.
the problem is:
ln 5+(1/2)ln y-3ln(z+1)
and the problem says 'rewrite expression as a single logarithm.
thanks for your help
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Note: ln (lowercase "L" then "n") is a natural log. It is a logarithm with base e = 2.718... (this is a special logarithm). This means that ln%28x%29+=+log%28e%2C%28x%29%29


ln%285%29+%2B+%281%2F2%29%2Aln%28y%29+-+3%2Aln%28z%2B1%29

ln%285%29+%2B+ln%28y%5E%281%2F2%29%5E%22%22%29+-+ln%28%28z%2B1%29%5E3%29

ln%285%29+%2B+ln%28sqrt%28y%29%29+-+ln%28%28z%2B1%29%5E3%29

ln%285%2Asqrt%28y%29%29+-+ln%28%28z%2B1%29%5E3%29

ln%28%285%2Asqrt%28y%29%29%2F%28%28z%2B1%29%5E3%29%29

Therefore ln%285%29+%2B+%281%2F2%29%2Aln%28y%29+-+3%2Aln%28z%2B1%29 condenses to ln%28%285%2Asqrt%28y%29%29%2F%28%28z%2B1%29%5E3%29%29
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