SOLUTION: I am having problems remembering domains. I need to find the domain of the following: f(t) = log(t-5) Is the domain (-infinity, +infinity)?

Algebra ->  Algebra  -> Logarithm Solvers, Trainers and Word Problems -> SOLUTION: I am having problems remembering domains. I need to find the domain of the following: f(t) = log(t-5) Is the domain (-infinity, +infinity)?      Log On

Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   

Question 132312: I am having problems remembering domains. I need to find the domain of the following:
f(t) = log(t-5)
Is the domain (-infinity, +infinity)?
Answer by jim_thompson5910(21667) 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%2810%2C%28t-5%29%29 (just replace t with x), we get
+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+log%2810%2C%28x-5%29%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