What is the number 212three in base-two form?

I think the correct given number is 212 base 3 and we are asked to convert this number into base 2.

We should recall that a number let us say X with a base of Y can also be written as:

X base Y = log X / log Y

Therefore in this case, the new number base should be equal to the initial number base. That is:

log 212 / log 3 = log X / log 2

So let us find for X:

log X = (log 212 / log 3) * log 2

X = 10 ^ [ (log 212 / log 3) * log 2]

X = 10 ^ (1.467754511

X = 29.36

Therefore the new form would be:

29.36 base 2