Solving Simultaneous Equations Using Logarithms

[synkk]

Homework Statement

Solve the simultanious equations
$$2log_2y = log_43 + log_2x$$
$$3^y = 9^x$$

The Attempt at a Solution

$$3^y = (3^2)^x$$
$$y = 2x$$

$$2log_2 x + 2log_2 2 = log_2 \sqrt{3} + log_2 x$$
$$log_2 x = log_2 \frac{\sqrt{3}}{4}$$


No idea what to do from where, what does x equals?

 

[grzz]

Correct up to now.
The only steps that remain to be done is to use

2log(...) = log[(...)$^{2}$] and

logu + logv = log (uv)

 

[Mark44]

If log_ax = log_ay, then x = y.

 

[synkk]

Ah okay, thank you guys.