Question 288337
The reference to "sums/differences" should bring to mind two of the properties of logarithms:<ul><li><{{{log(a, (p*q)) = log(a, (p)) + log(a, (q))}}}</li><li><{{{log(a, (p/q)) = log(a, (p)) - log(a, (q))}}}</li></ul>
{{{log(17, (x^3y^5/z^4))}}}
We can start by using the second property, because of the division:
{{{log(17, (x^3y^5)) - log(17, (z^4))}}}
And now the first property because of the multiplication:
{{{log(17, (x^3)) + log(17, (y^5)) - log(17, (z^4))}}}
This may the the desired answer. Or you could use a third property, {{{log(a, (p^q)) = q*log(a, (p))}}}, to move the exponents out in front:
{{{3log(17, (x)) + 5log(17, (y)) - 4log(17, (z))}}}