SOLUTION: Find the domain of f(t)=log(t-5)

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Question 147641: Find the domain of f(t)=log(t-5)

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

log%2810%2C%28t-5%29%29 Start with the given expression

Remember you cannot take the log of zero or of a negative value. So that means the argument t-5 must be greater than zero (i.e. the argument must be positive)

t-5%3E0 Set the inner expression greater than zero

t%3E0%2B5Add 5 to both sides


t%3E5 Combine like terms on the right side


So that means t must be greater than 5 in order for t to be in the domain

So the domain in set-builder notation is


So here is the domain in interval notation:


Notice if we graph y=log%28t-5%29 (just replace t with x), we get
+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+log%2810%2Cx-5%29%29+ notice how the graph never crosses the line x=5. So this graphically verifies our answer.

and we can see that x must be greater than 5 in order to lie on the graph