Question 930331
<pre>
{{{log((x^3*sqrt(x+1)/(x-2)^2))}}}

First use the rule: {{{log((A/B))=log(A)-log(B)}}} with {{{A=x^3*sqrt(x+1)}}} and {{{B=(x-2)^2}}}.  So we have:

{{{log((x^3*sqrt(x+1))-log(((x-2)^2)))}}}

Use the rule {{{log(A*B)=log(A)+log(B)}}} on the first term with {{{A=x^3}}} and {{{B=sqrt(x+1)}}}

{{{log((x^3))+log((sqrt(x+1)))-log((x-2)^2))}}}

{{{matrix(2,4,"","","","",Write,sqrt(x+1), as,(x+1)^(1/2) )}}}

{{{log((x^3))+log((x+1)^(1/2))-log((x-2)^2))}}}

Use the rule {{{log((A^B))=B*log((A))}}} on all three terms:

{{{3*log((x))+expr(1/2)*log((x+1))-2*log((x-2)))}}}

Edwin</pre>