Question 198954
{{{2ln(9)-5ln(x)+5ln(x^2+9)}}} Start with the given expression.



{{{ln(9^2)-ln(x^5)+ln((x^2+9)^5)}}} Rewrite the logs using the identity  {{{y*ln(x)=ln(x^y)}}}



{{{ln(81)-ln(x^5)+ln((x^2+9)^5)}}} Square 9 to get 81



{{{ln(81)-ln(x^5(x^2+9)^5)}}} Combine the logs using the identity {{{ln(A)+ln(B)=ln(A*B)}}}



{{{ln(81/(x^5(x^2+9)^5))}}} Combine the logs using the identity {{{ln(A)-ln(B)=ln(A/B)}}}




So {{{2ln(9)-5ln(x)+5ln(x^2+9)=ln(81/(x^5(x^2+9)^5))}}}