SOLUTION: How would you find the domain of : h(x)=3-2log base 4 {(x-2)-5} Doman had always been one of my worst enemies :((((( so any help would be greatly appreciated

Question 1031775: How would you find the domain of :
h(x)=3-2log base 4 {(x-2)-5}
Doman had always been one of my worst enemies :(((((
so any help would be greatly appreciated
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
you can't take the log of a negative number or 0, therefore the expression within the log function sign has to be greater than 0.

this means that (x-2)-5 has to be greater than 0.

(x-2)-5 is the same as x-7 so you get x-7 has to be greater than 0.

this means that x has to be greater than 7.

here's the graph of that equation.

$$$

there is an asymptote at x = 7.

the graph is only valid when x > 7.

this is because you can't take the log of a negative number or 0 and get a real answer that can be graphed on the real plane.

log((x-2)-5) = log(x-7).

x-7 > 0 results in x > 7.

your domain is all real values of x such that x > 7.

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