The domain of a function is all the "allowed" x values. Here, that side to side movement, or domain, of the function is found within the set of parenthesis with the x. The number outside the parenthesis, the -1 here, is up and down movement, or range. So the format for the side to side movement in an expression, is (x-h), where h is the x coordinate of our starting point on this graph. Since our side to side is (x+1), that would fit into our expression as (x-(-1)), so it moves 1 to the left of the original starting place, which is x = 0. Therefore, the domain is [tex]x \geq -1[/tex]. Now for the expansion...when you have a quotient, you expand a log by subtracting the denominator from the numerator, like this, in your case: [tex]log _{5} ( 7^{5} - 10^{3} )[/tex]. Depending upon how far you need to go with this, the simplification from above would be this: [tex]log _{5} (16807-1000)[/tex]. If you needed to solve that, it would start like this: [tex]log _{5} (15807)=x[/tex]. In exponential form we would rewrite as [tex] 5^{x} =15807[/tex]. Now take the log of both sides to bring down that x: [tex]log 5^{x} =log(15807)[/tex]. Following the properties of logs, we can bring down the x to get this: x log5 = log(15807). Solving for x means we divide both sides by log5 to find that x = 6.00
