Question 768771
<pre>
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.
{{{ln (sqrt(5)) - ln(25)}}}
= {{{ln(sqrt(5)/25)}}}    --> from rule 1 above
Call this eqn (A)

Now look at what you have inside the brackets.
{{{sqrt(5)/25}}} = {{{(5^(1/2))/5^2}}}
={{{5^((1/2) - 2)}}}    -----> remember that (a^m)/(a^n) = a^(m - n)
= {{{5^(-3/2)}}}

Now going back to eqn A
{{{ln(sqrt(5)/25)}}}
= {{{ln (5^(-3/2))}}}
= {{{(-3/2) * ln (5)}}}  ------> from rule 3 above

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