Uncertainties

Hey!

If I have a value, say 5.4±0.3, and I need to log the value so I could plot a log graph using it, would I also need to log the uncertainty, or how would the uncertainty change?

Thanks!

Reply 1

h3cat1

You need to calculate the logarithm of both the actual value and the uncertainty as follows:
ln(5.4) +/- ln(0.3)

Reply 2

nabsers

Original post by h3cat1

You need to calculate the logarithm of both the actual value and the uncertainty as follows:
ln(5.4) +/- ln(0.3)

Brilliant, thank you!

Reply 3

nabsers

Just wondering, how would this same operation work for a fractional or percentage uncertainty? Would you also log the fractional or percentage uncertainty as you do with the absolute uncertainty?

Reply 4

h3cat1

You cannot use logarithmic values when you are dealing with fractional or percentage uncertainty. The logarithmic value needs to be converted to the usual value before using it.

Original post by nabsers

Just wondering, how would this same operation work for a fractional or percentage uncertainty? Would you also log the fractional or percentage uncertainty as you do with the absolute uncertainty?

Reply 5

username3249896

if y = 5.4±0.3
ln y = 1.69±0.06

x = ln y
dx/dy= 1/y
so dx = dy/y
so error = 0.3/5.4 = 0.06

0.06 is not equal to ln 0.3

Reply 6

Eimmanuel

Study Forum Helper

Original post by nabsers

Hey!

If I have a value, say 5.4±0.3, and I need to log the value so I could plot a log graph using it, would I also need to log the uncertainty, or how would the uncertainty change?

Thanks!

Original post by h3cat1

You need to calculate the logarithm of both the actual value and the uncertainty as follows:
ln(5.4) +/- ln(0.3)

I would suggest that you plot a ln graph instead of a log graph. They are equivalent. Calculating the uncertainty using ln function is also “slightly easier”.

For A level, you can just apply the following calculation: