Hello,

I am trying to find a group homomorphism from $\displaystyle ( \mathbb{Z} /7 \mathbb{Z})^x \rightarrow \mathbb{Z} / 6 \mathbb{Z}$

After looking at it for a while, I noticed that $\displaystyle \phi = ln(x)$ works

i.e $\displaystyle ln(x * y) = ln(x) + ln(y)$

This is a property of logarithms. Can I just justify it that way?

Also if the homorphism went from $\displaystyle \mathbb{Z} / 6 \mathbb{Z} \rightarrow \mathbb{Z} /7 \mathbb{Z})^x$ , we have $\displaystyle \psi = e^x$?

Thank you for your help.