Asked by ENIS
Find the smallest values for a and b so that 21 base a equals 25 base b.
Answers
Answered by
Reiny
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
= 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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