Posted by **ENIS** on Friday, March 15, 2013 at 7:48pm.

Find the smallest values for a and b so that 21 base a equals 25 base b.

- math -
**Reiny**, Friday, March 15, 2013 at 8:19pm
21 using base a

= 2a + 1

25 using base b

= 2b+5

2a+1 = 2b+5

2a = 2b+4

a = b+2

in any base system for numbers, the base > 1

so the smallest value of b = 2

then a = 4

The smallest values are a=4, b=2

check:

21 base 4 = 2(4)+1 = 9

25 base 2 = 2(2) + 5 = 9

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