Interperating a graph with logarithmic scales

Also, you can try using a log table to find more accurate values for the logarithms. Remember, the logarithm is just the exponent on the base 10 that gives you the number you're taking the logarithm of. In summary, the conversation discusses using logarithms to find the duration of time between two points on a logarithmic scale. The suggested method involves finding the number of intervals between the points and using that value as the logarithm. More precise answers can be obtained by using a ruler and referencing a log table.
  • #1
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Homework Statement


see attachment


Homework Equations


log10x=y
10y=x


The Attempt at a Solution


Since I'm rather confused on reading a logarithmic scale, I thought I'd post this to see if I'm doing this right and/or if there's a better way to do the problem.

a) T=500 C
using the # of intervals we can say that if d=.01, x=.5 intervals so...
log(t)=.5
t=3.16 min

similarly for d=.1
log(t)=3.5 intervals
t=3162

change in time = 3162-3.16 = 3158.8min

b) same process but use x=-.5 intervals and x=2.1

If this method does work, is there any way to interpolate values so I can be more exact? or is there a better way to do the problem in general?
thanks!
 

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  • #2
I think you're on the right track, but maybe just a little off. For the 500 degree track (part a), the starting time is about 3.2 min, but the ending time looks to me like about 3.6, which corresponds to about 4000 min. Subtracting gives a duration that's again close to 4000 min. Unless you can really measure the position of the points very precisely, it doesn't make sense to end up with answers with more than one or two places of precision.
 
  • #3
yah, I was worried about being able to get a precise enough answer to matter. I think later I'll find a ruler and figure out more exact data points
thanks!
 
  • #4
Yes, a ruler would help you get more precise answers.
 

1. What is a logarithmic scale?

A logarithmic scale is a type of scale used on graphs that displays the values on the axis in a non-linear way. Instead of evenly spaced intervals, the values increase by a certain factor, such as 10 or 100.

2. How do I read a graph with a logarithmic scale?

To read a graph with a logarithmic scale, you must pay attention to the spacing of the values on the axis. The values increase by a certain factor, so the distance between 1 and 10 will be the same as the distance between 10 and 100. This allows for a wider range of values to be displayed on the graph.

3. Why are logarithmic scales used?

Logarithmic scales are used when the data being displayed has a large range of values. This allows for a more accurate representation of the data, as it prevents smaller values from being squished together and becoming difficult to read.

4. How do I determine the relationship between variables on a logarithmic scale?

To determine the relationship between variables on a logarithmic scale, you must look at the slope of the line on the graph. If the line is increasing, the relationship is positive (direct), and if the line is decreasing, the relationship is negative (inverse). The steeper the slope, the stronger the relationship.

5. Can a logarithmic scale be used for any type of data?

A logarithmic scale can be used for a wide range of data, including numerical and scientific data. However, it is important to consider the type of data being displayed and whether a logarithmic scale is appropriate for accurately representing the data.

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