log base 2 of x + log base 4 of x = 6

The change of base formula is $\log_b a = \frac{\log_c a}{\log_c b}$. We will change $\log_4 x$ to base 2.

$$\log_4 x = \frac{\log_2 x}{\log_2 4}$$

Since $2^2 = 4$, we know that $\log_2 4 = 2$.

$$\log_4 x = \frac{\log_2 x}{2}$$

Let $y = \log_2 x$.

$$y + \frac{y}{2} = 6$$ $$\frac{2y}{2} + \frac{y}{2} = 6$$ $$\frac{3y}{2} = 6$$

Multiply both sides by 2:

$$3y = 12$$

Divide both sides by 3:

$$y = 4$$

$$\log_2 x = 4$$

Convert the logarithmic equation to an exponential equation. If $\log_b a = c$, then $b^c = a$.

$$x = 2^4$$ $$x = 16$$

The final answer is 16.