Question

Domain of log equations questions.
Help please!

y=log(9-x^2)
y=log(x^2 +4)

Answer 1

@jim_thompson5910

Answer 2

you can't take the log of a negative number

you can't take the log of 0

Answer 3

so for log(x), the domain is x > 0

Answer 4

for log(9-x^2), the domain is 9-x^2 > 0

solve for x to get the answer for the first question

Answer 5

for log(x^2 +4), the domain is x^2 +4 > 0

solve for x to get the answer for the second question

Answer 6

so u get -3 or 3 is greater than x for the first one
and get -2 or 2 for the second one right?

Answer 7

we have to write the answer in interval notation so would I right (-3, infitity)?

Answer 8

9-x^2 > 0

leads to

-3 < x < 3

which in interval notation is (-3, 3)

Answer 9

x^2 +4 is ALWAYS positive because x^2 is ALWAYS nonegative and you're adding on a positive number

so x^2 +4 > 0 has the solution set of {x| x is any real number}

So that in interval notation is (-infinity, infinity)

Answer 10

I dont understand the first answer. How did it lead to -3 < x < 3?

Answer 11

9-x^2 > 0

9 > x^2

x^2 < 9

sqrt(x^2) < sqrt(9)

|x| < 3

-3 < x < 3

Answer 12

@jim_thompson5910

Answer 13

i just showed you

Answer 14

in general

sqrt(x^2) = |x| where x is any real number

and

|x| < k has the solution: -k < x < k where k is any positive number

Answer 15

oh okay. culd u help with a few more?

Answer 16

sure one more

Answer 17

okay log(base 3)(x/x-1)

Answer 18

@jim_thompson5910

Answer 19

finding the domain?

Answer 20

yes

Answer 21

and that's \(\Large \frac{x}{x-1}\) right?

Answer 22

yes but there is a base 3 before it

Answer 23

oh i'm just focusing on the stuff inside the log

Answer 24

\(\Large \frac{x}{x-1}\) is only positive when...

a) x and x-1 are both positive

OR

b) x and x-1 are both negative

Answer 25

x and x-1 are both positive

means

x > 0 and x > 1

which compresses to

x > 1

Answer 26

x and x-1 are both negative

means

x < 0 and x < 1

which compresses to

x < 0

Answer 27

so...


\(\Large \frac{x}{x-1}\) is only positive when...

a) x > 1

OR

b) x < 0

Answer 28

how does that help us find the domain?

Answer 29

not sure..

Answer 30

well you can't take the log of a negative number or zero, so \(\Large \frac{x}{x-1}\) must be positive

it's only positive when x > 1 or x < 0 as described above

so the domain in interval notation is (-infinity, 0) U (1, infinity)