Question 374256
{{{log(5, ((120*125)/24))}}}
First, let's reduce the fraction:
{{{log(5, ((24*5*125)/24))}}}
{{{log(5, ((cross(24)*5*125)/cross(24)))}}}
{{{log(5, (5*125)))}}}
Since {{{125 = 5^3}}} this becomes:
{{{log(5, (5*5^3)))}}}
{{{log(5, (5^4)))}}}
If you understand logarithms we already know that this works out to be 4. If not, then we can use a property of logarithms, {{{log(a, (p^q)) = q*log(a, (p))}}}, to move the exponent out in front:
{{{4*log(5, (5)))}}}
By definition, {{{log(5, (5)) = 1}}}. So this becomes:
4*1
or 
4