# Domain of g(x) = log (x + 3), g(t) = ln(t - 1) (check ans.)

#### Missy

##### New member
I wanted to see if I had this domain correct:

1: g(x) = log (x + 3)

my answer is x is greater than -3 which is the domain because I need a number that is bigger than -3

2: g(t) = In(t - 1)

my answer is that t is less than -1 since there can be no negative numbers.

Can you tell if I got these to equations correct?

Thank you Missy :?

#### jwpaine

##### Full Member
Missy said:
I wanted to see if I had this domain correct:

1: g(x) = log (x + 3)

my answer is x is greater than -3 which is the domain because I need a number that is bigger than -3

2: g(t) = In(t - 1)

my answer is that t is less than -1 since there can be no negative numbers.

Can you tell if I got these to equations correct?

Thank you Missy :?
ln is the one and only log.

g(x) = log (x + 3) ----> -3 < x < infinity : All reals greater than -3
g(t) = In(t - 1) ----> 1 < t < infinity : All reals greater than 1, because if we do n < 1 ln(n - 1) we get a non-real result... but ln(1 - 1) = ln(0) = infinity is ok

#### Missy

##### New member
Thank you very much for checking this out for me.
Missy

#### Mrspi

##### Senior Member
For the second one, g(t) = ln(t - 1) is NOT defined if (t - 1) <= 0.

so,

t - 1 > 0

t > 1

The domain for this function is all real numbers greater than 1.

#### stapel

##### Super Moderator
Staff member
jwpaine said:
ln(0) = infinity is ok
Not in many (most?) algebra texts. :shock:

Eliz.

#### jwpaine

##### Full Member
Re:

stapel said:
jwpaine said:
ln(0) = infinity is ok
Not in many (most?) algebra texts. :shock:

Eliz.
Errr.......for extremely large values of zero 