Question 630479
Use the properties 
{{{ln(a^n)=n*lna}}},
{{{ln(a*b)=lna+lnb}}}
{{{ln(a/b)=lna-lnb}}}
{{{lne=1}}}
.
{{{((ln x)^3 - ln (x^4))/((ln(x/e^2))ln(xe^2))=((ln x)^3 - 4lnx)/((lnx-ln(e^2))(lnx+ln(e^2)))=((ln x)^3 - 4lnx)/((lnx-2lne)(lnx+2lne))=((ln x)^3 - 4lnx)/((lnx-2)(lnx+2))}}}
.
 Use the formula {{{(a-b)(a+b)=a^2-b^2}}}
{{{((ln x)^3 - 4lnx)/((lnx-2)(lnx+2))=((ln x)^3 - 4lnx)/((lnx)^2-4)}}}
.
Since {{{ln x=t}}}
.
{{{((ln x)^3 - 4lnx)/((lnx)^2-4)=(t^3-4t)/(t^2-4)=t(t^2-4)/(t^2-4)=t}}}
.
Answer: {{{t}}}