Question 240493
{{{ln((3x^2)/(sqrt(2x+1)))}}} Start with the given expression.



{{{ln(3x^2)-ln(sqrt(2x+1))}}} Break up the log using the identity {{{ln(x/y)=ln(x)-ln(y)}}}



{{{ln(3)+ln(x^2)-ln(sqrt(2x+1))}}} Break up the first log using the identity {{{ln(xy)=ln(x)+ln(y)}}}



{{{ln(3)+ln(x^2)-ln((2x+1)^(1/2))^""}}} Convert to rational exponent notation.



{{{ln(3)+2*ln(x)-(1/2)ln(2x+1)}}} Pull down the exponents using the identity {{{ln(x^y)=y*ln(x)}}}



So {{{ln((3x^2)/(sqrt(2x+1)))=ln(3)+2*ln(x)-(1/2)ln(2x+1)}}}