How many 4-digit numbers are there in the decimal system, which have exactly 4-digits when expressed in Base 6, Base 7 and Base 8?
Answers
Given :4-digit numbers are there in the decimal system, which have exactly 4-digits when expressed in Base 6, Base 7 and Base 8
To find count of numbers
Step-by-step explanation:
4digits numbers in decimal systems
1000 to 9999
4 digits numbers in base 6
1000 to 5555 in base 6
value of 5555 in base 6 in decimal system would be
5x 6^3 + 5×6^2 + 5 × 6^1 + 5 × 6^0
= 1080 + 180 + 30 + 5
= 1295
or simply n digit number maximum value in base b is
n^b - 1
hence 6^4-1 = 1295
7^4 - 1 = 2400
8^4 - 1 = 4095
10^4 - 1 = 9999
hence from 1000 to 1295 numbers are there in the decimal system, which have exactly 4-digits when expressed in Base 6, Base 7 and Base 8
hence 296 numbers
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