Question

Log base 7 (3x-11) find domain and write in interval notation

Answer 1

\[\log_{7}(3x-11) \]

Answer 2

can you tell me what the domain is for y=log(x)?

Answer 3

0? or infinity?

Answer 4

it is a range of numbers
not just one number

Answer 5

Then I am lost, sorry

Answer 6

how about a graph of log(x)=y
recall the domain is the set of x values where the relation (function in this case) exists

Answer 7

looking at my graph for y=log(x)
can you tell me for what x values the function exists?

Answer 8

at 3 or 4? cant tell without numbers

Answer 9

myininaya is showing that the graph of ln(x) exists only for x>0

ln(0) will give you a math error on your calculator.
that is because
e^x =0 is not true for any x

Answer 10

ok that vertical line represents x=0
look at that graph it continues for much greater x values

Answer 11

ok

Answer 12

So it will be infinite positive numbers until we reach x?

Answer 13

the set is positive numbers
or you could say (0,infinity)

Answer 14

both of these say things that we can only have positive numbers for our domain

anyways we are looking at y=log(f(x))
we need f(x) to be positive which means we need f(x)>0

Answer 15

so 3x-11>0?

Answer 16

omg you took the words right out of my mouth
good job

Answer 17

solve that for x and you are done

Answer 18

well i guess you are also require to put it in interval notation after that

Answer 19

Lol sometimes words just confuse me. I am better with numbers i feel. so if i can find the proper way to set it i can complete it you know?

Answer 20

And yes. Can you explain to me how do go about doing so? My first guess would be (11/3,infinity)

Answer 21

that is right

Answer 22

To review,
the domain of a function are the numbers it "accepts" (without causing an error or being undefined). Lots of functions have a domain of all real numbers. Some, like the log, only accept numbers bigger than zero.

Answer 23

Lol thank u guys, i feel so slow until i actually get going. can I try one more with u to make sure i got it?

Answer 24

do you want me to make up one or do you have one?

Answer 25

I am taking practice problems from the book so i have one.

Answer 26

\[\log (x-5)+\log(8-.5x)\]

Answer 27

This might seem very elementary but when there is no base it is recognized as 10 right?

Answer 28

yes

Answer 29

this is another domain
question?

Answer 30

yea

Answer 31

you can go about this two different ways

you can find the domain of log(x-5) and the domain of log(8-.5x)
and then find the intersection of those sets to find the domain of log(x-5)+log(8-.5x)

or

you can find condense into one log and then remember that if you have y=log(f(x))
the domain is f(x)>0

Answer 32

do you know what i mean by intersection?

Answer 33

Im pretty sure i do. I think id like the first way a little better.

Answer 34

so what is the domain of log(x-5)?

Answer 35

5

Answer 36

the domain of a function are the numbers it "accepts"

Answer 37

\[-\infty,5\]

Answer 38

so can i ask what inequality you solved to get that?

Answer 39

uh oh lol , means im wrong

Answer 40

x-5=0

Answer 41

is that an inequality?

Answer 42

Dangit
x-5>0?

Answer 43

ok great
and you added 5 on both sides right
do you know how to read x>5?

Answer 44

like what does that mean?

Answer 45

All numbers greater than 5 are allowed?

Answer 46

so you mean to say the domain of log(x-5) is (5,inf)?

Answer 47

inf=infinity

Answer 48

Yes, i think lol

Answer 49

it is
(5,inf) means 5 and any number after 5 without actually including 5

Answer 50

so any number after 5 lol