I don't completely understand how logarithmic equations work...please help!
Find the domain of the function:
f(x)=log(sub2)(36-x(squared))
f(x)=log(sub10)(x+6/x-5)
The domain of a log function must always be greater than 0. This means you can solve what is being taken to 0 and find values for which the domain cannot be:
Using your first example:
$\displaystyle 36-x^2 = 0$
This is the difference of two squares with a = 6 and b =x
$\displaystyle (6-x)(6+x) = 0$
$\displaystyle x = \pm6$
Therefore values between -6 and 6 is the domain, to put it another way:
$\displaystyle -6< x < 6$ or $\displaystyle |x| < 6$