Number bases: Range of bases and searching for a number base

Questions
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1

Dear all,

I know how to convert numbers from one base to another in Wolfram|Alpha, e.g. “123456789_10 to base 2”. But I have not found a way to successfully tell WA the following tasks/questions:

  • Convert 123456789_10 to all bases from 2 to 45
  • Calculate the base x so that 100_10 is 83_x

Kind regards,

Franz

2

That latter could be something like solve 83=x^4+x or solve 10010=8x+3
depending on which you intended as the decimal and which the base-x numeral.