# Thread: Relationship between ln2, ln3, ln6

1. ## Relationship between ln2, ln3, ln6

1) How are the results for ln2, ln3, and ln6 related?
2) How are the results for ln20, ln5, ln4 related?
3) How are the results for ln3 and ln3^5 related?

...Can someone perhaps give me a hint as to what direction I'm supposed to approach this question from? What kind of relation am I looking for here?

2. since ln(x) is a strictly increasing function

1. ln2 < ln3 < ln6

also because ln(a) + ln(b) = ln(ab)

ln2 + ln3 = ln6

2. same here:

ln4 < ln5 < ln20

ln4 + ln5 = ln20

3.one of the properties of the ln function is: ln(a^b) = b*ln(a)

ln(3^5) = 5*ln3

Natural logarithm - Wikipedia, the free encyclopedia

3. I imagine they are wanting you to write an equation to relate the quantities. In other words use additon, subtraction, multiplication, division, exponentiation, etc. You will need to know properties of logarithms.

For the first one $\displaystyle \ln(3) + \ln(2) = \ln(6)$

4. Ah, that makes perfect sense. Thanks!