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jmc

number theory intermediate

Problem

What is the base ten equivalent of

1234 5_{6}

?

Solution

1234 5_{6} = 5 \cdot 6^{0} + 4 \cdot 6^{1} + 3 \cdot 6^{2} + 2 \cdot 6^{3} + 1 \cdot 6^{4} = 5 + 24 + 108 + 432 + 1296 = 1865

.

Final answer

1865