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A certain integer has 4 digits when written in base 8. The same integer has d digits when written in base 3. What is the sum of all possible values of d?

 Apr 20, 2022
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A certain integer has 4 digits when written in base 8.     Let the mumber be y

8^3=512      8^4=4096

In base 10                                  512 <= y < 4096

 

 

The same integer has d digits when written in base 3. What is the sum of all possible values of d?

3^5 = 243       4 digits

3^6 = 729        5 digits

3^7 = 2187      6 digits

3^8 = 6561      too big

 

so it could have 4, 5 or 6 digits in base 3 

 Apr 21, 2022
edited by Melody  Apr 21, 2022

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