Number transformers
Level: Advanced (score: 4)
Inspired by the movie Transformer, John decides to design a "number transformer" as a test.
It is capable to perfom the transformation of the number 1 (one is the base) to any "target" number.
The two allowed operations/rules are:
 multiply by 2
 int divide by 3
The operations can be chained repeatedly, and maybe just needs to run one of the rules.
Let's see an example:

Convert 1 (base number) to 10 (target number) = 6 operations:
1 * 2 * 2 * 2 * 2 // 3 * 2 = 10

Convert 1 (base number) to 8 (target number) = 3 operations:
1 * 2 * 2 * 2 = 8
After some manual testing with a few small numbers, it seems to be working just fine.
But what about bigger numbers? What if the number is greater than 10?
Can you help him to design a function to mearsure the efficiency, aka, how many operations it will take to convert 1 (the base) to the asking target number?
[Hint] the data structure is the key here.