Shaswat221005
contestada

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

Respuesta :

konrad509

[tex] \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) [/tex]

So, the least [tex] n [/tex] is 7.

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