How Do You Express the Number of Security PINs in Logarithmic Form?

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SUMMARY

A security PIN code consists of four digits, each ranging from 0 to 9, resulting in a total of 10,000 possible combinations. To express the number of security PINs in logarithmic form with base 10, the formula is derived as y = log10(10,000). This simplifies to y = 4, confirming that there are 4 digits in the PIN code. The discussion clarifies the reasoning behind the logarithmic expression and the calculation of possible combinations for varying digit lengths.

PREREQUISITES
  • Understanding of logarithmic functions and their properties
  • Basic knowledge of combinatorics and counting principles
  • Familiarity with base 10 number system
  • Ability to manipulate algebraic expressions
NEXT STEPS
  • Study logarithmic identities and their applications in combinatorics
  • Learn about permutations and combinations in discrete mathematics
  • Explore the concept of exponential growth and its relation to logarithms
  • Investigate real-world applications of PIN codes and security measures
USEFUL FOR

Students studying mathematics, particularly in algebra and combinatorics, as well as professionals in cybersecurity and systems design who require an understanding of PIN code generation and security protocols.

BlackOut07
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Homework Statement



A security PIN code is four digits long. Each digit could have the value 0 to 9. if an office building needs 10 security PINs, express the number of codes in logarithmic form with base 10


The Attempt at a Solution



y=4log(x-10)

I don't know how to do the question, but my best attempt produced what you see above.

4 represents the # of digits.
x-10 because of the range 0-9.
 
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What was your reasoning behind "x- 10"?

There are [itex]10^1= 10[/itex] one digit numbers, 0 to 9.

There are [itex]10^2= 100[/itex] two digit numbers, 00 to 99.

There are [itex]10^3= 1000[/itex] three digit numbers, 000 to 999.
 

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