Question 244644
Log Rules that you should learn:

1) {{{logb(mn) = logb(m) + logb(n)}}}

2) {{{logb(m/n) = logb(m) – logb(n)}}}

3) {{{logb(m^n) = n · logb(m)}}}



Assuming log3 means log(base 3):

{{{3 log3X + 4 log3Y-4log3Z }}}
{{{log3x^3+log3Y^4-log3Z^4}}} Using rule 3
{{{log3 (x^3*y^4)/z^4}}} Using rule 1 and 2

{{{2(3 ln x-ln(x+1)-ln(x-1))}}} 
{{{2( ln x^3-ln(x+1)-ln(x-1))}}} Using rule 3
{{{2( ln ((x^3/(x+1))/(x-1)))}}} Using rule 2
{{{ln (x^3/((x+1)*(x-1)))^2}}} Using rule 3 
{{{ln (x^6/((x+1)^2*(x-1)^2))}}}