# How do you find the domain of #C(x)=ln((x+3)^4 )#?

##### 1 Answer

The domain of

#### Explanation:

Assuming we're dealing with the Real natural logarithm, the domain is

When

#(x+3)^4 = ((-3)+3)^4 = 0^4 = 0#

and

So

When

#(x+3)^4 > 0#

so

So the domain is the whole of the Real numbers except

In interval notation

**Footnote**

The interesting thing about this question is the immediate temptation to turn:

#C(x) = ln((x+3)^4)#

into:

#C(x) = 4 ln(x+3)#

While this would be true for any

In fact, if you extend the definition of

#ln t = ln abs(t) + pi i" "# (principal value)

and hence if

#4 ln (x+3) = 4 (ln abs(x+3) + pi i) = 4 ln abs(x+3) + 4 pi i != 4 ln abs(x+3) = ln ((x+3)^4)#