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# Logarithms are useful in representing numbers by their magnitudes.
There are many scales that experimenters use that are in logarithmic scales. Such as decibels for intensity of sound, Richter for intensity of earthquakes, and pH for acidic concentration.
One possible reason is a quantity is noticeably different when it differs by a factor.
![[---images/---assets/---icons/question-icon.svg]] Consider the following two diagrams, one of them has more points than the other one. They differ by 10 points in fact, one has $N$, and the other has $N+10$. Determine which is which.
![[1 teaching/summer program 2023/week 3/---files/Pasted image 20230829052747.png]]
Now below are two diagrams, one of them has mroe points than the other, they differ by a factor of 10 in fact, one of them has $N$, and the other one has $10N$. Determine which is which.
![[1 teaching/summer program 2023/puzzles-and-problems/---files/Pasted image 20230829073033.png]]
![[---images/---assets/---icons/question-icon.svg]] The following depicts two sets of points in five boxes. They all start from 100 points.
One of these sets form an arithmetic sequence with a common difference of 100.
One of these sets form an arithmetic sequence with a common difference of 200.
One of these sets form an arithmetic sequence with a common difference of 500.
One of these sets form a geometric sequence of common ratio of 2.
One of these sets form a geometric sequence of common ratio of 5.
Can you tell which is which?
(a)![[1 teaching/summer program 2023/puzzles-and-problems/---files/Pasted image 20230829075151.png]]
(b)![[1 teaching/summer program 2023/puzzles-and-problems/---files/Pasted image 20230829075113.png]]
(c)![[1 teaching/summer program 2023/puzzles-and-problems/---files/Pasted image 20230829075219.png]]
(d)![[1 teaching/summer program 2023/puzzles-and-problems/---files/Pasted image 20230829075130.png]]
(e)![[1 teaching/summer program 2023/puzzles-and-problems/---files/Pasted image 20230829075308.png]]