SOLUTION: how do I solve ln e^1.5-ln square root e

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Question 112334: how do I solve ln e^1.5-ln square root e
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
ln%28e%5E1.5%29-ln%28sqrt%28e%29%29 Start with the given expression


ln%28e%5E1.5%29-ln%28e%5E%281%2F2%29%29 Rewrite sqrt%28e%29 as e%5E%281%2F2%29



ln%28e%5E%283%2F2%29%29-ln%28e%5E%281%2F2%29%29 Rewrite 1.5 as 3%2F2


%283%2F2%29ln%28e%29-%281%2F2%29ln%28e%29 Rewrite the logarithms using the identity ln%28x%5Ey%29=y%2Aln%28x%29


%283%2F2%29%2A1-%281%2F2%29%2A1 Now take the natural log of e to get 1. Remember ln%28e%29=1



3%2F2-1%2F2 Simplify


2%2F2 Subtract


1 Reduce


So ln%28e%5E1.5%29-ln%28sqrt%28e%29%29=1