Question 311997
<pre><b>
What you got is what the answer would have been if
the sign of the third term had been " - " and not " + ". 

Here's the right way. Pay close attention to the signs
and the log rules:

{{{10log((x))-7log((y))+5log((z))}}}

Use the rule {{{A*log((C))=log((C^A))}}} on all three terms,
to change the coefficients to exponents:

{{{log((x^10))-log((y^7))+log((z^5))}}}

Use the rule {{{log((A))-log((C))=log((A/C))}}}

to write the first two terms as the log of a quotient:

{{{log(((x^10)/(y^7)))+log((z^5))}}}

Use the rule {{{log((A))+log((C))=log((AC))}}}

to write those two terms as the log of a product:

{{{log((((x^10)/(y^7))(z^5)))}}}

Put the second factor in the parentheses over 1:

{{{log((((x^10)/(y^7))(z^5/1)))}}}

Multiply the two tope and the two bottoms:

{{{log(((x^10z^5)/(y^7)))}}}

Edwin</pre>