SOLUTION: I have not only spent the last four days, literally, on one assignment consisting of 7 sections all having to do with natural log, e, 10 and log. But anyhow, this one I have spent

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Question 768771: I have not only spent the last four days, literally, on one assignment consisting of 7 sections all having to do with natural log, e, 10 and log.
But anyhow, this one I have spent more than ten hours on by itself.
Write the expression as a logarithm of a single expression.
ln sqrt5 - ln25.
I have broke it down some, as far as I can get it: 5 ln^1/2 - ln 5 - ln 5.
I'm not entirely sure I understand how I got here.
But the answer in the book say's It's -3/2 ln 5=ln 5^-3/2
Were does the -3/2come from and how do I set this up
Found 2 solutions by lwsshak3, ramkikk66:
Answer by lwsshak3(11628)   (Show Source): You can put this solution on YOUR website!
ln sqrt5 - ln25
Answer by ramkikk66(644)   (Show Source): You can put this solution on YOUR website!


It's fairly simple if you remember the basic rules of logarithms.

1) Log a - log b = log (a/b) --> assume it is all to the same base e.g. ln.

2) log a + log b = log (a * b)

3) log (a^b) = b * log a



Now look at the problem.



=     --> from rule 1 above

Call this eqn (A)



Now look at what you have inside the brackets.

 = 

=    -----> remember that (a^m)/(a^n) = a^(m - n)

= 



Now going back to eqn A



= 

=   ------> from rule 3 above



Hope you got it now. Let me know if it is not clear :)



 

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