Question 196051
{{{7*ln(x)+4*ln(y)-3*ln(z)}}} Start with the given expression



{{{ln(x^7)+ln(y^4)-ln(z^3)}}} Take the coefficients and place them as exponents (just the absolute value of the coefficients)



Note: {{{y*ln(x)=ln(x^y)}}}



{{{ln(x^7*y^4)-ln(z^3)}}} Combine the logs using the identity {{{ln(A)+ln(B)=ln(AB)}}}



{{{ln((x^7*y^4)/(z^3))}}} Combine the logs using the identity {{{ln(A)-ln(B)=ln(A/B)}}}





So {{{7*ln(x)+4*ln(y)-3*ln(z)=ln((x^7*y^4)/(z^3))}}} where {{{x>=1}}}, {{{y>=1}}}, and {{{z>=1}}}