Range of x and y for ln(2+y) = 5ln(3-x) - 2√x

[feely]

Homework Statement

Real variables x and y are related by the equation

ln(2+y) = 5ln(3 - x) - 2 sqrt x ...(sorry, I haven't as yet got the hang on LaTeX)

Determine the range of values of x and y for which the expressions on each side of this equation are defined.

Homework Equations

The Attempt at a Solution

I haven't really been able to make an attempt at a solution. I think I have to take the exp of each side, but I am not sure excatly what way I go about this, so if someone could give me some advice, that would be fantastic.

Thanks in advance.

Sean

 

[Hootenanny]

HINTS:

(1) For what values of $\gamma$ is $\ln\gamma$ defined?

(2) For what values of $\eta$ is $\sqrt{\eta}$ defined?