Question 1016064: what is the domain of the function below?
f(x)=3log base 5(2x+6)-6
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i believe the only requirement here is that the expression that you are taking the log of must be greater than 0.
that means that 2x+6 must be greater than 0.
solve for x to get x has to be greater than -3.
if you graph this equation, you will see that the value of x can't be less than or equal to -3.
in other words, it has to be greater than -3.
the graph is shown below:
see below the graph for further comments.
from the graph, you can see that the line of the equation approaches x = -3 but will never touch it.
going to the right, the graph has no end.
the domain is therefore all real values of x such that x > -3.
in interval notation that would be x = (-3,infinity)
x can't be -3 because x = -3 would make the expression inside the log equal to 0 which it can't be.
x can't be infinity because infinity is not a number.
it's an expression that says that the right side of the graph goes on forever and has no end.
you can test this out by just supplying some number to your calculator.
in order to use the calculator, you need to convert the base of the log to base of 10 or base of e.
base of 10 is the log function of your calculator.
base of e is the ln function of your calculator.
log5(2x+6) would be entered as log(2x+6)/log(5) in your calculator.
log5(2x+6) can also be entered as ln(2x+6)/ln(5) in your calculator.
either one will allow your calculator to determine the value of log5(x).
we'll use the log function as an example.
3log5(2x+6)-6 would be entered as 3*log(2x+6)/log(5) - 6.
if your calculator can't handle entering 2x+6 as such, you would need to calculate the value of 2x+6 based on the value of x that you choose, and enter it that way.
when x = -3, this becomes 3*log(0)/log(5)-6, because 2*-3+6 -6+6 = 0.
enter that in your calculator and you get something that says you can't do that.
in my calculator (ti-84 plus), i enter 3*log(0)/log(5)-6 and get ERR:DOMAIN
it's a little cryptic but it means that i can't take the log of 0.
if i want to find the log of a positive number, i would do the same.
when x = 5 in my equation, the expression of 3 * log5(2x+6) - 6 becomes 3 * log5(16) - 6 which i would then enter as 3*log(16)/log(5)-6 and it would tell me that the answer is -.83188.
look on the graph and you will see that when x = 5, the value of the equation tells you the same thing.
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