In Exercises 75–80, find the domain of each logarithmic function....

Question

In Exercises 75–80, find the domain of each logarithmic function. f(x) = log5 (x+4)

Accepted Answer

Welcome back. I am so glad you're here. We are given the function F of X equals log six of X plus seven. And we are asked to solve for the domain of this function Alright. We do have a domain restriction whenever we have a log and whatever we're taking the log of. So in this case X plus seven must be greater than zero. So now let's solve for what values of X will make this statement true that X plus seven is greater than zero. Let's get X by itself will subtract seven from both sides. So on the left that's X. And it's greater than negative seven. We can think of this on a number line, so negative seven is our boundary and X can be any value greater than it. So it's heading off toward positive infinity. We need to put an open circle on negative seven because X has to be greater than negative seven, it can't be equal to it. And we draw our line up to the right. Alright, how do we express this? An interval notation? Will we start with a parentheses to indicate that it cannot be negative seven but starting just after negative seven. All the way up to positive infinity. And closing infinity with the parentheses as well to show that will never quite obtain infinity. We look at our answer choices in this matches with answer choice B. Well done, we'll catch you on the next one

In Exercises 75–80, find the domain of each logarithmic function. f(x) = log5 (x+4)

Key Concepts

Logarithmic Functions

Domain of a Function

Inequalities

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