Table of Contents
Last modified on May 25th, 2024
Semi-log graphs and log-log graphs are two different types of logarithmic graphs used for plotting statistical data with a wide range in magnitudes.
In a semi-log (or semi-logarithmic) graph, the y-axis is scaled logarithmically (the scales between the ticks on the graph are proportional to the logarithm of numbers), while the x-axis remains linear (the scales are evenly placed), making this graph a hybrid of the two scales.
However, semi-log graphs can also be represented with the logarithmic x-axis and the linear y-axis.
Now, plotting a function y = 2x on a linear scale as well as on a semi-log scale, we get:
Selecting some points of the x-variables and evaluating the values of the function, we get
x | 0 | 1 | 2 | 3 | 4 | 5 |
y = 2x | 20 = 1 | 21 = 2 | 22 = 4 | 23 = 8 | 24 = 16 | 25 = 32 |
Now, using the values, we get the graphs as follows:
Since the y-axis of the semilog graph contains only the logarithms of positive numbers, the negative numbers are not included in this graph.
It is useful for graphing exponential functions like y = abx, which produces a straight line with the slope of log(b) and the y-intercept of log(a).
Given is a blank printable version of the above Semi Log Graph for your use.
In a log-log (or double logarithmic) graph, both the x and y-axes use a logarithmic scale.
It is used to create population charts, Zipf distributions, and air pressure measurements.
Now, plotting a function y = x3 on an ordinary axis (where the x and y axes are linear) as well as on a log-log scale, we get:
Selecting some points of the x-variables and evaluating the values of the function, we get
x | 1 | 2 | 3 | 4 | 5 | 10 |
y = x3 | 13 = 1 | 23 = 8 | 33 = 27 | 43 = 64 | 53 = 125 | 103 = 1000 |
Now, using the values, we get the graphs as shown:
It is useful for determining power relationships between variables expressed in exponential form like y = axb, which produces a straight line with the slope ‘b’ and the y-intercept of log(a).
Given is a blank printable version of the above Log Log Graph for your use.
E.g.1. Plot f(x) = ${\sqrt{x}}$ on a log-log graph.
Here, f(x) = ${\sqrt{x}}$
Selecting some points of the x-variables and evaluating the values of the function f(x), we get
x | 1 | 4 | 9 | 16 | 25 | 100 |
f(x) | 1 | 2 | 3 | 4 | 5 | 10 |
Now, using the values, we get the following log-log graph.
E.g.2. Plot f(x) = ex on a semi-log graph.
Here, f(x) = ex
Selecting some points of the x-variables and evaluating the values of the function f(x), we get
x | 0 | 1 | 2 | 3 | 4 |
f(x) | 1 | 2.72 | 7.39 | 20.1 | 54.6 |
Now, using the values, we get the following semi-log graph.
Last modified on May 25th, 2024