Logarithm Base Question

Suppose you have a integer n. Log2(n) is supposed to be ~ the number of times you have to divide n by 2 until you reach one. Now let's say you want to know ~ the number of times you have multiply n by 2/3 until you reach one. What kind of logarithm would you have to evaluate to find that? Thanks, this came up when analyzing an algorithm.

Multiplying by $2/3$ is the same as dividing by $3/2$, so you want a logarithm to the base $3/2$.