Question 127412
{{{Ln(x)=2Ln(x)-Ln(y)+Ln(c)}}} Start with the given equation



{{{0=2Ln(x)-Ln(y)+Ln(c)-Ln(x)}}} Subtract Ln(x) from both sides



{{{Ln(y)=2Ln(x)+Ln(c)-Ln(x)}}} Add Ln(y) to both sides



{{{Ln(y)=Ln(x^2)+Ln(c)-Ln(x)}}} Now rewrite {{{2Ln(x)}}} as {{{Ln(x^2)}}} by using the identity {{{y*Ln(x)=Ln(x^y)}}}



{{{Ln(y)=Ln(x^2c/x)}}} Rewrite the right side by using the identities {{{Ln(x)+Ln(y)=Ln(x*y)}}} and {{{Ln(x)-Ln(y)=Ln(x/y)}}}



{{{Ln(y)=Ln(xc)}}} Simplify



{{{e^(Ln(y))=e^(Ln(xc))}}} Now raise both sides as powers with "e" as the base



{{{y=xc}}} Simplify. Remember, {{{e^(Ln(y))=y}}} (ie these two functions undo each other and cancel themselves out)