Solving SI Units with ln(n): A High School Puzzler

In summary, the conversation discusses using the ln function for a quantity, specifically n = 0.00149 kg/m*s. The result is approximately -6.51 + ln kg - ln m - ln s. However, there is confusion about what the ln of n represents and how to handle the SI units. Suggestions are given to convert to a dimensionless value before taking the logarithm and to use this as a double check for calculations.
  • #1
Const@ntine
285
18
I tried with Google but I couldn't find anything, so here goes: When I "use ln on a quantity" (I don't really know how to phrase it in english, as we just have a verb for it), say, I have n = 0.00149 kg/m*s, and I put it into the ln, so now I have ln(0.00149 kg/m*s) what happens to the SI Units? The result of 0.00149 ~-6.508, but I'm not sure on the kg/m*s. It never came up during HS so I now have to fill a board with the ln of various values of n, and I'm not sure what to do with SI.

Any help is appreciated!
 
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  • #2
The unwritten sign between ##0.00149## and ##\frac{kg}{m \cdot s}## is a multiplication. So ##\ln n \approx -6.51 + \ln kg - \ln m - \ln s## which can hardly be interpreted and thus raises the question: what do you want to express and what's the goal? What should ##\ln n## stand for? If it is only a scaling for some plot, then the units remain as they are, as only the graphic representation of the magnitude of ##n## changes, not the quantity.
 
  • #3
fresh_42 said:
The unwritten sign between ##0.00149## and ##\frac{kg}{m \cdot s}## is a multiplication. So ##\ln n \approx -6.51 + \ln kg - \ln m - \ln s## which can hardly be interpreted and thus raises the question: what do you want to express and what's the goal? What should ##\ln n## stand for? If it is only a scaling for some plot, then the units remain as they are, as only the graphic representation of the magnitude of ##n## changes, not the quantity.
Yeah, the first thing that popped to my mind was the classic ln(a*b) = lna + lnb as well.

In my case n is the viscosity index of a liquid (alcoholic, specifically). It's not used in any formula or anything, we just have to fill this board (it's for Lab), and for each n, we need the ln. I was just curious whether there was some "rule" about such cases.
 
  • #4
Normally, you would want to convert to some dimensionless value before you take the logarithm. This could be done by dividing by some arbitrary constant, which you could call n0.
 
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  • #5
Well, thanks a lot for the help everyone! I appreciate it.
 
  • #6
FYI, this is actually one way of double checking the validity of your calculations. If you suddenly find yourself taking the square root of for example 5kg, that very often shows something went wrong somewhere.
 
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  • #7
rumborak said:
FYI, this is actually one way of double checking the validity of your calculations. If you suddenly find yourself taking the square root of for example 5kg, that very often shows something went wrong somewhere.
Thanks for the info, I'll keep it in mind!
 

Related to Solving SI Units with ln(n): A High School Puzzler

What is the purpose of "Solving SI Units with ln(n): A High School Puzzler"?

The purpose of "Solving SI Units with ln(n): A High School Puzzler" is to help students understand how to convert units using the natural logarithm function, ln(n).

What is ln(n) and how does it relate to SI units?

ln(n) is the natural logarithm function, which is the inverse of the exponential function. It is commonly used in mathematics and science to solve for unknown values in equations. In relation to SI units, ln(n) can be used to convert between different units of measurement.

Why is it important for high school students to learn about SI units and ln(n)?

SI units are the international standard for measurement and are used in scientific and mathematical calculations. Understanding how to convert between different units using ln(n) is essential for accurate and precise measurements in these fields.

What are some common challenges students may face when solving SI units with ln(n)?

Some common challenges students may face include understanding the concept of logarithms, knowing when to use ln(n) versus other logarithmic functions, and making mistakes in calculations. It is important for students to practice and seek help if they are struggling with these concepts.

How can students apply their knowledge of SI units and ln(n) in real-world situations?

Students can apply their knowledge of SI units and ln(n) in various real-world situations, such as converting units of measurement in science experiments or calculating interest rates in finance. This skill is also useful in everyday life, such as converting between different units of currency or measuring ingredients for recipes.

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