Question 998827
if you want to do it in same base:

{{{log( p,root(5,sqrt((x-2)^8/(x(x+3)^2))))}}}

 {{{log( p,(((x-2)^8/(x(x+3)^2))^(1/2))^(1/5))}}}

{{{(1/5)log( p,(((x-2)^8/(x(x+3)^2))^(1/2))))}}} 


{{{(1/5)(1/2)log( p,(((x-2)^8/(x(x+3)^2)))))}}} 


{{{(1/10)(log( p,((x-2)^8)-log(p,(x(x+3)^2))))}}} 


{{{(1/10)(8log(p,(x-2))-(log(p,(x))+log(p,(x+3)^2)))}}} 


{{{(1/10)(8log( p,((x-2))-(log(p,x)-2log(p,(x+3)))))}}} 


{{{(1/10)(8log( p,((x-2))-log(p,x)+2log(p,(x+3)))))}}}


{{{(8log( p,(x-2)))/10-log(p,x)/10+(2log(p,(x+3)))/10}}}


{{{(4log( p,((x-2))))/5-log(p,x)/10+(log(p,(x+3)))/5}}}


or, if you need to change the base:


{{{log( p,root(5,sqrt((x-2)^8/(x(x+3)^2))))}}} 


{{{log( p,(((x-2)^8/(x(x+3)^2))^(1/2))^(1/5))}}}....in base {{{10}}} will be

 

{{{log((((x-2)^8/(x(x+3)^2))^(1/2))^(1/5))/log(( p))}}}



{{{(1/5)log( (((x-2)^8/(x(x+3)^2))^(1/2)))/log(( p))}}} 



{{{(1/2)(1/5)*log( (((x-2)^8/(x(x+3)^2))))/log(( p))}}} 



{{{(log( (x-2)^8)-log(x(x+3)^2))/10log(( p))}}}



{{{(8log((x-2))-(log(x)+2log(x+3)))/10log(( p))}}}


{{{(8log((x-2))-log(x)-2log((x+3)))/10log(( p))}}}


{{{8log((x-2))/10log(( p))-log(x)/10log(( p))-2log((x+3))/10log(( p))}}}


{{{4log((x-2))/5log(( p))-log(x)/10log(( p))-log((x+3))/5log(( p))}}}