Uncertainty with a log function

In summary, the conversation discusses finding the uncertainty for a log function, specifically f = 20log(V_in/V_out). The person is attempting to use calculus to find the uncertainty, but is unsure if their approach is correct. They also mention wanting a relative error, but are unsure how to handle the lack of units in the function. A link to a Wikipedia page on error propagation is provided as a potential resource.
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sprinks13
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Homework Statement


Im trying to find the uncertainty for a log function. I have that

f = 20log(V_in/V_out)

and i want to know (delta)f

Homework Equations



f = 20log(V_in/V_out)

The Attempt at a Solution



I was going to do it the calculus way:

f = 20log(V_in) -20log(V_out)

df = 20*f*[(dV_in/V_in) - (dV_out/V_out)]

but this doesn't seem right to me. I've never seen subtraction in an error calculation before. And I am not sure if this is a relative error or a percent error. I want a relative error (with units), the only problem is that my function has no units, soI'm not sure what I should do in that case (if that makes sense).

Is there another simple formula for log function errors?
 
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FAQ: Uncertainty with a log function

What is a log function and how does it relate to uncertainty?

A log function is a mathematical function that calculates the logarithm of a number. In the context of uncertainty, a log function is often used to represent the relationship between the uncertainty of a measurement and the actual value of the measurement. This can be seen in equations such as the log-normal distribution, where uncertainty is represented as a logarithmic standard deviation.

How is uncertainty typically represented in a log function?

Uncertainty is usually represented in a log function as a logarithmic standard deviation. This means that the uncertainty is proportional to the logarithm of the actual value. For example, if the uncertainty is represented as 1% of the actual value, it would be expressed as a logarithmic standard deviation of 0.01.

Can a log function accurately represent uncertainty?

Yes, a log function can accurately represent uncertainty when used in the proper context. It is commonly used in statistics and probability to represent the uncertainty of a measurement or data set. However, it is important to note that a log function may not be the best representation for all types of uncertainty.

What are the limitations of using a log function to represent uncertainty?

One limitation of using a log function to represent uncertainty is that it assumes a symmetrical distribution of uncertainty. This means that the uncertainty is equally likely to be above or below the actual value. In some cases, uncertainty may be skewed, making a log function a less accurate representation. Additionally, a log function may not be appropriate for all types of data and may not accurately represent extreme values of uncertainty.

How can we use a log function to make predictions about uncertainty?

A log function can be used to make predictions about uncertainty by analyzing the relationship between uncertainty and the actual value. By understanding the behavior of the log function, we can make informed predictions about how uncertainty may change as the actual value changes. This can be especially useful in forecasting and decision-making processes.

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