How do I approach this problem is the difficulty for me. If I can get a headstart then I'll be able to finished it from there. I got this problem for a junior at school, it say if $\log_3 (x-6) = 2y$ and $\log_2 (x-7) = 3y$
Show that $x^2 - 13x + 42 = 72^y$.
Now, from my own end I don't know what step to take that will lead me to the answer. Any help will be highly appreciated
well, from the definition of log, we obtain $$ \left\{ \begin{align*} x - 6 &= 3^{2y} = 9^y \\ x - 7 &= 2^{3y} = 8^y \end{align*} \right. $$
multiply both sides instantly generates what's desired.