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| Math Central | Quandaries & Queries |
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Question from Michael, a student: Let k be a positive integer so that 28 (subscript)k = 132 (subscript)5 |
Hi Michael,
You have a number expressed two different ways, one with base 5, $132_5$ and the other using base $k, 28_k .$ You can use what you know about expressing numbers in different bases to write them in base 10. For example $435_8$ means 5 plus 3 eights plus 4 eight squared. That is
\[435_8 = 5 + 3 \times 8 + 4 \times 8^2 = 5 + 24 + 256 = 285.\]
Use this method to write $132_5$ and $28_k$ in base ten, set them equal and solve for $k.$
Penny
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