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kondor19780726 [428]
2 years ago
9

An n-digit number is a positive number with exactly n digits. Nine hundred distinct n digit numbers are to be formed using only

three digit 5, 7, 9. The smallest value of n for which this is possible is :
(A) 6
(B)7
(C)8
(D)9
Mathematics
1 answer:
kolbaska11 [484]2 years ago
5 0

\underbrace{3\cdot3\cdot3\cdot\ldots}_{n}\geq900\\\\
3^n\geq900\\\\
\log_3 3^n\geq \log_3900\\\\
n\geq \log_3900\\\\
n\geq\dfrac{\ln 900}{\ln 3}(\approx6.2)

So, the least n is 7.

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