Exponential equation - logarithmisation is the transformation of this equation: $$9^x + 6^x = 2× 4^x$$
into this: $$\log_2 (9^x) + \log_2 (6^x)=\log_2 (2×4^x)$$ correct? I want to know because I really want to solve this equation.

No. One property of logarithms is that $\log(a) + \log(b) =\log(ab).$
So $\log(a + b)$ may not be reduced as you have done.
