Can someone tell me this is right?
Look for the domain.
f(x)=log(sub3)(5x+1)
5x+1<=0
(5x/5)<=(-1/5)
x<=(-1/5)
x>(-1/5)
(-1/5,oo) -domain
yes, x > -1/5
Thank-you!
actually your second line should have said
5x+1 > 0
I just looked at your answer.
Do I need to change it in each line after the second line?
Yes, your work is correct. The domain of the function f(x) = log₃(5x+1) is (-1/5, ∞).
To determine the domain, you need to consider the restrictions on the input values (x) of the function. In this case, we are dealing with a logarithmic function.
First, you recognize that the base of the logarithm is 3. Logarithms are defined only for positive values, so 3 > 0 implies that the expression inside the logarithm must be greater than 0.
Setting 5x+1 greater than 0, you get the inequality 5x+1 > 0. To solve this inequality, subtract 1 from both sides: 5x > -1. Then, divide both sides by 5: x > -1/5.
Hence, the range of x that satisfies the inequality is x > -1/5.
Finally, you express the domain using interval notation, which in this case is (-1/5, ∞), indicating that any value greater than -1/5 (including infinity) is allowed for x in the given function.