# Relationship between ln2, ln3, ln6

• March 24th 2008, 04:38 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?
• March 24th 2008, 04:45 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

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