# Thread: Logs and real variables.

1. ## Logs and real variables.

Hello, Iam hoping to get some help with a question I have for an assignment ...

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."

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.

Sean

2. Since powers of $\displaystyle e$ are always positive, the natural logarithm function $\displaystyle \ln\, x$ is only defined for positive values of $\displaystyle x$. Similarly, since squares are always nonnegative, the function $\displaystyle \sqrt{x}$ is only defined for nonnegative real numbers.

For $\displaystyle \ln\,(2 + y)$ to be defined, $\displaystyle 2 + y$ must therefore be positive.

For $\displaystyle 5\,\ln\,(3 - x) - 2\sqrt{x}$ to be defined, both terms must have a value and thus be defined individually. Therefore, $\displaystyle 3 - x$ must be positive, and $\displaystyle x$ must be nonnegative.

To view the LaTeX source code for any formula on this forum, you can click on it.

3. Thanks

I have it now. I thought it was more complicated than it was.

Cheers

Sean