### Instruction: Solve for $x:\ \log_2 x+\log_4 x= 6.$.### Response: So we have $\log_2 x+\log_4 x= 6.$
Yeah. Let's first convert $\log_4 x$ into $\log_2 x$.
To do that we use the change of base formula, which says $\log_a b=\frac{\log_c b}{\log_c a}$.
So we have $\log_2 x+\frac{\log_2 x}{\log_2 4}=6$.
Right. Now we simplify.
$\log_2 x+\frac{\log_2 x}{2}=6$
$\frac{3\log_2 x}{2}=6$
$\log_2 x=4$
So $x=2^4=16$.