# Relationship between ln2, ln3, ln6

• Mar 24th 2008, 03:38 PM
theowne
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?
• Mar 24th 2008, 03:45 PM
Peritus
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

you might also consider reading:

Natural logarithm - Wikipedia, the free encyclopedia
• Mar 24th 2008, 03:46 PM
iknowone
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 $\ln(3) + \ln(2) = \ln(6)$
• Mar 24th 2008, 03:50 PM
theowne
Ah, that makes perfect sense. Thanks!