Applications of Indices Surds and Logarithms

Question

A bacterial colony B with the initial mass of 2 picogram will increase every day, that is 3 times the mass of the previous day. Find the time, in the nearest day, that will be taken by the bacterial colony B to become 15 pg.

Answer 1

m = m₀3^t. So, 15 = 2·3^t, 3^t = 7.5, t = ln7.5/ln3 = 1.834 ≈ 2 days.

Answer 2

15 = 2(3)^t

7.5 = 3^t

ln 7.5 = t ln 3

Can you solve for t and answer?