In the number system with some base, the decimal number ’59’ is written as 324

In the number system with some base, the decimal number ’59’ is written as 324 In which system is the number written?

Since the largest digit in the number is 4, the base of the number cannot be less than 5.

The number 324 in base 5 in decimal system corresponds to the number 3 * 5 ^ 2 + 2 * 5 + 4 = 75 + 10 + 4 = 89.

If the base is greater than 5, the decimal number will be even greater.

Conclusion: in none of the possible number systems does the number 324 correspond to the decimal number 59.