Solving $2^x + 3^x = 12$ I need to solve $2^x + 3^x = 12$ for real $x$. I tried the following:
$$
2^x + 3^x = 3\times 2^2 \\
1+(3/2)^x= 3\times 2^{2-x}
$$
But from here on I don't know how to apply logarithms.

Value of $x=1.917685944888545$
(15 digits round off)

