#1**+1 **

3 = k 2^r and 15 = k 2^2r

Multiply first equation by 5 and equate the two equations

NOTE: k 4^2 = k (2^2)^r = k 2^{2r}

5 k 2^r = k 2^2r divide out k

5 * 2^r = 2^2r take log of both sides

log 5 + r log 2 = 2r log 2

log 5 = r (2log2 - log2)

log5 / log 2 = r = 2.321928095 (and k = 3/5)

ElectricPavlov Aug 7, 2020

edited by
ElectricPavlov
Aug 7, 2020

edited by ElectricPavlov Aug 7, 2020

edited by ElectricPavlov Aug 7, 2020

edited by ElectricPavlov Aug 7, 2020

edited by ElectricPavlov Aug 7, 2020

#3**+1 **

Guess I did too many steps in my head and lost ya

15 = k 4^r = k * (2^2)^r = k * 2^2r

ElectricPavlov
Aug 7, 2020