Homework Help: Logarithms help

1. Dec 8, 2011

synkk

1. The problem statement, all variables and given/known data
Solve the simultanious equations
$$2log_2y = log_43 + log_2x$$
$$3^y = 9^x$$

3. 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?

Last edited by a moderator: Dec 8, 2011
2. Dec 8, 2011

grzz

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

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

logu + logv = log (uv)

3. Dec 8, 2011

Staff: Mentor

If logax = logay, then x = y.

4. Dec 8, 2011

synkk

Ah okay, thank you guys.