The Power of X

Algebra Level 4

$\large 9^X = 6^X + 4^X \quad,\quad X = \ ?$

\log_{\frac32}\left( \frac{1+\sqrt5}2\right)

\frac { 1+\sqrt { 5 } }{ 2 }

None of the rest

\log_{\frac23}\left( \frac{1+\sqrt5}2\right)