Question 272850
{{{(1/2)*ln(x)+4*ln(y)-3*ln(z)}}} Start with the given expression.



{{{ln(x^(1/2)^"")+ln(y^4)-ln(z^3)}}} Use the identity {{{y*ln(x)=ln(x^y)}}}



{{{ln(sqrt(x))+ln(y^4)-ln(z^3)}}} Convert to radical notation.



{{{ln(sqrt(x)*y^4)-ln(z^3)}}} Combine the first two logs using the identity {{{ln(x)+ln(y)=ln(xy)}}}



{{{ln(y^4*sqrt(x))-ln(z^3)}}} Rearrange the terms.



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



So {{{(1/2)*ln(x)+4*ln(y)-3*ln(z)=ln((y^4*sqrt(x))/z^3)}}} where each variable is greater than zero.