Find the value of x if (23)_x = 111100010₂

I've converted it into decimal, which is 482.

 

But that's where I get stuck.

 

Any ideas?

You need to break down 23 or any number in a place-holder system. The number 576 in decimal is interpreted without thinking - but what does it represent?

 

[math] 576_{10} = (5*10^2) + (7*10^1) + (6 *10^0) [/math]

 

in general

 

[math] 576_x = (5*x^2) + (7*x^1) + (6 *x^0) [/math]

 

You can then just rearrange your question into a nice polynomial which you solve for x. That said I must be missing something cos I cannot get yours to work - maybe I am just having a brain fade.

Imfataal, the reason you're having trouble is:

Assuming his radix is an integer.

[math]23_x = 2x + 3 = 2(x+1) + 1 = 2n+1 [/math] Is odd.

[math]111100010_2[/math] is even.

 

Either his radix is not an integer (rational solution to [math]2x+3 = 482[/math]) or there's a transcription error somewhere.

Edited July 24, 201213 yr by Schrödinger's hat