Thread: Finding range of ln equation. Without calculator

1. 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

2. 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 $\displaystyle x+3 > 0$.

3. What is the range of $\displaystyle \ln x$ ?

4. An easy way to remember the range of the natural log is to recall that $\displaystyle ln|a| = x \implies$ $\displaystyle a = e^x$.

5. its (-inf, inf) so all real numbers?

6. 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.