The reason the “Excel logarithmic scale doesn’t start at 0” is that the log zero value is undefined. A number like this cannot be a real number, because anything raised to the power of another number will never become zero. There is no way to reach zero, only to approach it with infinitely large and negative power. In this article, we describe the reason for the fact that the “Excel logarithmic scale doesn’t start at 0”. Let’s follow the complete guide to learn all of this
What Is Logarithm?
The logarithm can be defined as a number raised to a certain power to arrive at some other number. Large numbers are easily expressed through the logarithm. For instance, we can express logarithm like the following.
Here,
- a and b re real numbers (positive).
- A log base is situated at the bottom of the log. Here, a is the base.
- The log contains an argument called b.
There are two types of logarithms. One is a common logarithm and the other is a natural logarithm.
Common Logarithm
Common logarithms are base 10 logarithms, which are represented as Log10 in mathematics.
For instance, the logarithm of 10000 is expressed as log(10000). This common logarithm indicates the number of times we need to multiply ten in order to determine desired output.
For instance, log(10000)=4
That mean, if we multiply ten 4 times, we will get the value 10000.
Natural Logarithm
Natural logarithms, on the other hand, are expressed as base e logarithms, which are represented by loge. This natural logarithm indicates the number of times we need to multiply e in order to determine desired output.
For instance, ln(2)=0.693
Is It Possible to Start Logarithmic Scale at 0?
Log scales allow numerical data to be displayed over a broad range of values compactly. We want to show the reason “Excel logarithmic scale doesn’t start at 0”. It is impossible to start the logarithmic scale at zero.
Like the following image, if we want to put zero value in the LOG function, we will get an undefined value. In Excel which means error.
If we want to draw a chart of the dataset at the logarithmic scale we will never get starting of the log scale at zero. For demonstration purposes, we want to show a log chart in Excel. To draw the log chart we have to follow the following steps.
📌 Steps:
- To create a chart, select the range of data and go to the Insert tab. Next, select the Recommended charts.
- Next, select All Charts > Column.
- As a result, you will get the following chart.
- To convert the chart into a log chart, you have to right-click on the y axis value and select Format Axis.
- When the Format Axis window appears, check Logarithmic Scale.
- As a result, you will get the following logarithmic chart.
- To modify the chart style, select Chart Design and then, select your desired Style9 option from the Chart Styles
- Finally, you will get the following logarithmic chart.
From the above chart, we can see that the logarithmic scale starts at one not at zero. So we can say that it is impossible to start the logarithmic scale at zero because log 0 provides us with an undefined value. This is the reason for the fact that the “Excel logarithmic scale doesn’t start at 0”.
Read More: How to Plot Log Scale in Excel
Why LOG(0) Shows #NUM! Error in Excel?
Here, we will answer the most important question “what is the value of logarithm zero?”
In Excel, if we put zero as an argument in the LOG function we get an error like the following picture. Because the value log0 is not defined. It is showing #NUM! error.
The reason behind this fact is that we can define the logarithm function only for the argument whose value is greater than zero. For instance, we express logarithm as shown below.
Here, the logarithm function defined for b>0
Here, the base a logarithm of 0 is not undefined.
The base 10 logarithms of zero are undefined. For instance, log10(0) is undefined.
Again, in the case of approaching zero from the positive side(0+), the limit of this log function returns minus infinity.
Read More: How to Log Transform Data in Excel
Minimum Value to Start a Logarithmic Scale
To get the value of the logarithm function as a positive real number, the argument value must be greater than one. If we put the argument value zero in the logarithm function we will get zero. On the other hand, if we put the argument value more than one, we will get a positive real number.
For instance, we can express logarithm like the following.
To get the value of the logarithm function as a positive real number the augment b must be greater than one.
📌 Steps:
- We will use the following formula in the cell C5:
=LOG(B5)
The LOG function returns the logarithm of a number to the base we specify.
- Then, press Enter.
- Next, drag the Fill Handle icon
- As a result, you will get the following logarithm function value.
From the above picture, we get the value of LOG(1) is zero. When we put the argument value above, we get a real number. For instance, if we enter argument value 1.1 we will get the LOG(1.1) value 0.04139269.
Now, if we enter a negative number as an argument, we will get undefined by using the logarithm function. In the following picture, we can see that the logarithm of the negative number shows an error.
Last but not least, the argument value for the logarithm function must be greater than one in order to get its value as a positive real number.
If we enter the number between 0 and 1 as an argument will get the value logarithm as a negative real number. In the following image, we can see log(0.5) shows the value -0.30103. Similarly, log(0.0001) returns -4.
So, if we want to get a negative logarithm value, we need to put an argument between 0 and 1.
Read More: How to Calculate Logarithmic Growth in Excel
Value of Logarithm 1
By using the LOG and LN functions we can the value of logarithm 1. Because the log 1 value is zero, the logarithm of 1 is always zero, regardless of the logarithmic base. All numbers raised to 0 equal 1 by definition. Thus, ln1=0
In the following picture, we can see that if we use the following function LOG1 we will get the value zero.
we will use the following formula in the cell C4:
=LOG(1)
The LOG function returns the logarithm of a number to the base we specify.
In the following picture, if we use the following function LN1 we will get the value zero.
we will use the following formula in the cell C5:
=LN(1)
The LOG function returns the natural logarithm of a number.
Value of Logarithm of Infinity
What we will get from the log(infinity)?
log10(∞) =?
To get the value of the logarithm of infinity, we need to use limits as infinity isn’t a number.
b Is Approaching Infinity
We can get the value of the limit of the function log(b) is infinity while b approaches infinity.
b Is Approaching Minus Infinity
Similarly, the log (minus infinity) (-∞) is not defined, since negative numbers have an unknown logarithmic function.
The value of the above limit is undefined.
Download Practice Workbook
Download this practice workbook to exercise while you are reading this article.
Conclusion
That’s the end of today’s session. I strongly believe that from now you may know the reason why “Excel logarithmic scale doesn’t start at 0”. If you have any queries or recommendations, please share them in the comments section below.
Keep learning new methods and keep growing!
