A number theory problem on bases.

762 5 x = 11111001010 1 2 7625_x = 111110010101_2

The equation above shows 7625 in base x x equals 111110010101 in base 2. What is x ? x?


The answer is 8.

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1 solution

Marta Reece
Jul 24, 2017

Number 7625 7625 in base x = 111 110 010 101 x=111\space 110\space 010 \space 101 in base 2 2 .

I have divided the number in base 2 2 into four groups of three digits each.

If the individual groups are interpreted as numbers in base 2 2 , they are 7 , 6 , 2 , 7, 6, 2, and 5 5

Each triplet is one digit in base x = 2 3 = 8 x=2^3=\boxed8

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