Question 490264
There are three basic properties of logarithms:
{{{log(p,(a*b)) = log(p, (a)) + log(p, (b))}}}
{{{log(p,(a/b)) = log(p, (a)) - log(p, (b))}}}
and
{{{log(p,(a^b)) = b*log(p, (a))}}}<br>
{{{ln(8/e^4)}}}
Since the argument of you logarithm is a quotient (division), we can use the second property on your logarithm:
{{{ln(8) - ln(e^4)}}}
Since the argument of the second logarithm is an exponential term, we can use the third property on it:
{{{ln(8) - 4*ln(e)}}}
And finally, since {{{log(a, (a)) = 1}}} for ALL bases and since the base for ln is e, ln(e) = 1. So the expression simplifies to:
{{{ln(8) - 4*1}}}
or
{{{ln(8) - 4}}}