Question 470545
{{{ln(z^5/root(3,( x^5y^5)))}}}
Use formulas {{{ln(a*b)=ln(a)+ln(b)}}}, {{{ln(a/b)=ln(a)-ln(b)}}},{{{ln(a^n)=n*ln(a)}}}
{{{ln(z^5/root(3,( x^5y^5)))=ln(z^5)-ln(root(3,( x^5y^5)))=5ln(z)-ln((x^5y^5)^(1/3))=5*ln(z)-(1/3)ln(x^5y^5)=5*ln(z)-(1/3)(ln(x^5)+ln(y^5))=5*ln(z)-(1/3)(5ln(x)+5ln(y))=5*ln(z)-(5/3)lnx-(5/3)lny}}}
Answer: c. 5lnz-5/3lnx-5/3lny