Question 198952
{{{log(10,(x))+(1/4)log(10,(x^2+1))+5log(10,(x-1))}}} Start with the given expression.



{{{log(10,(x))+log(10,((x^2+1)^(1/4)))+log(10,((x-1)^5))}}} Rewrite the logs using the identity  {{{y*log(b,(x))=log(b,(x^y))}}}



{{{log(10,(x))+log(10,(root(4,x^2+1)))+log(10,((x-1)^5))}}} Convert to radical notation.



{{{log(10,(x*root(4,x^2+1)*(x-1)^5))}}} Combine the logs using the identity {{{log(b,(A))+log(b,(B))=log(b,(A*B))}}}



So {{{log(10,(x))+(1/4)log(10,(x^2+1))+5log(10,(x-1))=log(10,(x*root(4,x^2+1)*(x-1)^5))}}}