Question

\[f(x)=\log_{(x-3)} (x-2)-\log_{(x-3)}(x^2+3x-10) \]
What values of x will produce a defined function? (Domain)

Answer 1

do you know where is undefined the logarithm ?

Answer 2

and you need to know the property of log. like


log(a) x - log(a) y = log(a) x/y

hope these will help you sure

Answer 3

and the next step you can rewriting factorizing

x^2 +3x -10 = (x -2)(x+5)

Answer 4

I know that in logs for a function to be defined you must have: \[\log_{a} (b)\]
a>0, a=/=1
b>0

Answer 5

f(x)=log_(x-3)(x-2)-log_(x-3)(x^2+3x-10)
f(x)=[log(x-2)-log(x^2+3x-10)]/log(x-3)
f(x)=[log(x-2)-log((x-2)(x+5))]/log(x-3)
f(x)=-log(x+5)/log(x-3)
the domain
{x belongs to R:3<x<4 or x>4}