Question 374255
I'm not sure what "law of logarithms" is so thsi may not be what you are looking for.<br>
{{{log(5, (1000/8))}}}
First we'll simplify the argument. 1000/8 = 125:
{{{log(5, (125))}}}
{{{125 = 5^3}}} so this becomes:
{{{log(5, (5^3))}}}
If you understand what this logarithm stands for then you know that this simplifies to 3. If not, then we can use a property of logarithms, {{{log(a, (p^q)) = q*log(a, (p))}}}, to move the exponent of the argument out in front:
{{{3*log(5, (5))}}}
Since {{{log(5, (5)) = 1}}} by definition, this becomes:
3*1
or
3