# Finding range of ln equation. Without calculator

• Jul 29th 2010, 09:33 PM
danielh9103
Finding range of ln equation. Without calculator
i know the domain is (-3 , infinity)

y = ln(x+3)

i thought it was [-4, infinity) but i checked on a calculator and it goes passed -4. And i cannot use a calculator
• Jul 29th 2010, 09:52 PM
lvleph
The range of a function is the set of numbers the function can achieve. The natural log has a range $\displaystyle (-\infty,\infty)$. However, its domain is $\displaystyle (-3,\infty)$. The domain is the set of numbers for which the function is defined. Natural log can take numbers from $\displaystyle (0,\infty)$. So we just need to check when $\displaystyle x+3 > 0$.
• Jul 29th 2010, 09:53 PM
pickslides
What is the range of $\displaystyle \ln x$ ?
• Jul 29th 2010, 11:50 PM
Math Major
An easy way to remember the range of the natural log is to recall that $\displaystyle ln|a| = x \implies$ $\displaystyle a = e^x$.
• Jul 30th 2010, 10:24 AM
danielh9103
its (-inf, inf) so all real numbers?
• Jul 30th 2010, 11:46 AM
eumyang
Yep!

It may be helpful to remember from now on that the domain of the basic f(x) = ln x is (0, ∞) and that the range is (-∞, ∞). In my textbook it's considered one of the twelve basic functions.