There is a Equation: $2^x + 3^x = 6^x + 6$.
I tried to do a lot of thing but I couldn't solve this equation.
one of the thing that I do:
I assume that
$t_1 = 2^x$ so $\log_2 t_1 = x$
$t_2 = 3^x$ so $\log_3 t_2 = x$
$t_3 = 6^x$ so $\log_6 t_3 = x$
so we have
$t_1 + t_2 = t_3 + 6$ and
$\log_2 t_1 = \log_3 t_2 = \log_6 t_3 = \log_6 t_1*t_2$
Then I try lots of way to solve my equation with this method but nothing happen!
Is it possible to help me to solve this? I'm sorry for bad English too.