Question

Please Help!
Find the domain and range.
f(x)=log3(x-2)+3

Answer 1

\(\large\color{black}{ \displaystyle f(x)=\log_3(x-2)+3}\)

Answer 2

you can't take a log of 0, or of any negative number.
That would mean that x-2 has to be greater than 0

Answer 3

For x-2 to be greater than 0

x-2>0
x>2

Answer 4

got the domain part ?

Answer 5

yes how would I get the range

Answer 6

ok, for that follow along with me...

Answer 7

Tell me what is
(lets disregard the base 3, since it doesn't do anything in our case)

what is \(\large\color{black}{ \displaystyle \log(0.1)}\) ?

Answer 8

-1

Answer 9

hint: \(\large\color{black}{ \displaystyle \log(0.1)}\) >> \(\large\color{black}{ \displaystyle \log(\frac{1}{10})}\) >> \(\large\color{black}{ \displaystyle \log(10^{-1})}\) >> \(\large\color{black}{ \displaystyle -\log(10)}\) >> \(\large\color{black}{ \displaystyle -1}\)

Answer 10

correct

Answer 11

What is \(\large\color{black}{ \displaystyle \log(0.01)}\) ?

Answer 12

Its hard to read it seems you retyped a few things
can you explain better

Answer 13

I didn't re-type anything.

Answer 14

I am just trying to get to the following:

\(\large\color{black}{ \displaystyle \log(0.1)=\log(10^{-1})=-1}\)
\(\large\color{black}{ \displaystyle \log(0.01)=\log(10^{-2})=-2}\)
\(\large\color{black}{ \displaystyle \log(0.001)=\log(10^{-3})=-3}\)
\(\large\color{black}{ \displaystyle \log(0.0001)=\log(10^{-4})=-4}\)
\(\large\color{black}{ \displaystyle \log(0.00001)=\log(10^{-1})=-5}\)

and on....

Answer 15

and the closer the input approaches 0, the more magnitude the negative value gains

Answer 16

ok thank you how do I get the range from it

Answer 17

\(\large\color{black}{ \displaystyle 1\times 10^{-\infty}}\) is a very very very small number (that apprahces zero and closer and closer to zero, the bigger this infity gets.

right ?

Answer 18

yes

Answer 19

that means, the closer x gets to zero, smaller value you are plugging in log(x)

Answer 20

however
when you plug this very small value into log(x) what what happens.

\(\large\color{black}{ \displaystyle \log\left(x\right)}\)
\(\large\color{black}{ \displaystyle \log\left( 10^{-\infty}\right)}\)
\(\large\color{black}{ \displaystyle -\infty~\log\left( 10\right)}\)
\(\large\color{black}{ \displaystyle -\infty}\)

Answer 21

So, as far as negative values go, log(x) can get as 'small' as \(\large\color{black}{ \displaystyle -\infty)}\)

Answer 22

so how would this effect my equation

Answer 23

Isn't range just all the y values

Answer 24

and can you get to the positive infinity range when having log(x) ?

Answer 25

yes, range is all values of y

Answer 26

I was trying to get first, to why this is so.

Answer 27

yes
just not 0 or negative right?

Answer 28

it can be 0

Answer 29

the range can be zero or negative

Answer 30

\(\large\color{black}{ \displaystyle \log(1)=0}\)
(no matter what the base is)

\(\large\color{black}{ \displaystyle \log(A)}\)
when A<0
that gives a negative range

Answer 31

ok but how do I use my equation to find the range