1. ## Logarithmic Equation

Find the domain of the function:

f(x)=log(sub2)(36-x(squared))

f(x)=log(sub10)(x+6/x-5)

2. Originally Posted by kanej316

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:

$36-x^2 = 0$

This is the difference of two squares with a = 6 and b =x

$(6-x)(6+x) = 0$

$x = \pm6$

Therefore values between -6 and 6 is the domain, to put it another way:

$-6< x < 6$ or $|x| < 6$