logarithmic question

Question

Let p = ln(2), q = ln(3), and r = ln(5). Write ln(3.3repeating) in terms of p,
q, and r

Answer 1

p = ln(2)

e^p = 2

 

q = ln(3)

e^q = 3

 

r = ln(5)

e^r = 5

 

3.333... = 2*5/3 = e^p*e^r/e^q = e^p+r-q

 

ln(3.333...) = ln(e^p+r-q) = p + r - q