Answer to Question #197512 in Algebra for Avelile

Question

prove ln(xy)=ln(x)+ln(y)

Answer 1

$\textbf{Prove:}$

Let $ln(xy)=c, ln(x)=a, ln(y)=b$, then

$e^{c}=xy, \, e^{a}=x, \, e^{b}=y.$

$e^{a+b}=e^{a}e^{b}=xy=e^{c}\Rightarrow a+b=c$ or $ln(x)+ln(y)=ln(xy)$.