# What are logarithmic price scales and how are they used?

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Usually, in technical analysis, it is recommended to use logarithmic price scales, although in practice they are rarely used. Linear charts are used by most traders.

In this article, we will answer the question: What are logarithmic price scales? Why are they so important? Is it an analysis worth doing? What is it used for?

## What are logarithmic price scales?

Logarithmic price scales charts, also known as semi-log scales or logarithmic scales, are a type of financial chart used in trading and investing. They display price movements on a logarithmic scale for one axis (usually the vertical axis) and a linear scale for the other axis (typically the horizontal axis).

The logarithmic scale on one axis represents price movements in percentage terms rather than absolute price changes. In a logarithmic scale, equal distances represent equal percentage changes.

For example, on a semi-log chart, a move from £10 to £20 would look the same as a move from £100 to £200, as both represent a 100% increase.

The opposite of a logarithmic price scale t is a linear scale, or chart. In a linear chart, both the vertical and horizontal axes use linear scales, representing price movements and time intervals in their numerical values.

Unlike logarithmic price scales that show percentage changes in price, linear charts display price changes as they are in absolute terms.

### Example of linear scale vs logarithmic price scale

If we buy a share for £100 and sell it for £200, the profit will be £100. In percentage terms, the return on investment is 100%.

If an investor buys a share for £200 and sells it for £300, they would make a profit of £100. This is the same return as in the previous example in monetary terms, although in percentage terms the profit was only 50%.

These two price jumps are represented the same in a linear chart, although in percentage terms or in return on investment they are different. In a linear chart, investing £100 and earning £200, and investing £200 and earning £300 is represented exactly the same.

A logarithmic scale corrects this mistake by showing the actual percentage (i.e., 100% vs 50%).

## What is chart analysis?

Chart analysis is a way of analysing data and trends by visualising them in order to identify patterns and useful information.

This means that it is used to study price movements in the past to predict possible future outcomes.

The goal of chart analysis is to draw conclusions about market behaviour using different tools such as lines, and channels, among other elements.

### What does logarithmic mean?

Logarithmic refers to a mathematical concept that involves logarithms. Logarithms are a way to represent the relationship between numbers in a specific way.

In simple terms, a logarithm of a number is the exponent to which another fixed number (called the base) must be raised to produce that number. For example, in base 10 logarithms, the logarithm of 100 is 2 because 10 raised to the power of 2 equals 100 (i.e., 10^2 = 100).

They compress larger values into a more manageable scale, making it easier to analyse and visualise data that spans a wide range of magnitudes. In finance, logarithmic scales are often used to display percentage changes or price movements over time, allowing for clearer visualisation and analysis of trends.

## What are logarithmic price scales?

Logarithmic price scales are a type of chart that combines both linear and logarithmic elements at the same time.

They are designed to allow the user to visualise changes on two different scales at the same time.

The horizontal axes (x) display numbers on a logarithmic scale, while the vertical axes (y) display numbers on a linear scale.

### How is a logarithmic scales used?

A logarithmic price scale is used to plot data separated by large intervals. The axes of the chart are scaled logarithmically instead of the usual linear increment.

This means that, although the underlying data may vary widely from each other, they will appear as a smooth curve when plotted on a logarithmic chart. This makes it useful for quick and easy representation of various complex numbers (for example, extreme temperatures) without distorting them too much.

## Linear scale vs. logarithmic price scale

Linear scales and logarithmic price scales are two types of charts used in trading. Both have their advantages and disadvantages, so the choice between them depends on the specific objective for which they are used.

Linear graphs show a more general representation of the data, taking as a reference the relationship between prices at a given time and their variation over time.

This way of visualising data provides the trader with a complete overview of market behaviour.

A major disadvantage is that they do not clearly show significant trends due to random daily fluctuations. In addition, they are subject to distortions when there are extremely large ups and downs within a short period (market volatility).

Logarithmic price scale in trading are a useful tool for traders. These types of charts allow the trader to see the price action at different price levels, which allows them to make more informed trading decisions.

They are also useful because they help identify trend patterns and possible entry or exit points. In general, traders use logarithmic price scales frequently due to their unique characteristics and potential benefits.

## Are logarithmic price scales convenient for analysing Bitcoin?

Yes, logarithmic charts are often used for analysing Bitcoin and other cryptocurrencies due to their unique price movements.

Bitcoin has experienced extremely volatile price changes over its history, with significant increases and decreases in value. A logarithmic price scale helps in visualising these price movements more effectively compared to a linear chart.

Cryptocurrency markets, including Bitcoin, often exhibit long-term trends that might be challenging to interpret on a linear scale due to their extreme price fluctuations. A logarithmic price scale helps in identifying and analysing these trends more clearly over extended periods.

Also, traders use support and resistance levels to make trading decisions. Logarithmic price scales charts can reveal these levels more effectively, helping traders identify potential entry or exit points.

### How to read and analyse a Bitcoin price chart?

To read and analyse a Bitcoin price chart, it is important to understand the information being presented. Charts generally show the price of Bitcoin over time, so the first steps involve identifying the time frame in which the measurements are taken and what values they represent.

Once this is done, patterns in the data can be identified to determine how the price has changed over time.

This includes identifying upward or downward trends, significant high and low points, previous historical highs, and much more.

In addition to studying the main price line, if there are other indicators such as volume or volatility available to examine, they can be used to gain a better understanding of the market and its dynamics over time.

## What is a logarithmic scale?

A logarithmic scale is a measurement scale in which each point represents relative changes rather than absolute differences.

Logarithmic price scales compress large ranges of values, especially those covering several orders of magnitude, into a more manageable visual space. This compression allows for better visualisation and analysis of data that spans a wide range of magnitudes.

### What is a logarithmic price scale?

Instead of being presented with linear values (1, 2, 3, 4…), the data in a logarithmic scale chart are presented as powers of a number (10^0 = 1; 10^1 = 10; 10^2 = 100).

This allows for visualising significant changes between very different quantities. A typical example would be comparing the total area of separate countries and states using the same chart.

## What are relative scales?

Relative scales are a type of measure that is used to compare values, placing them in relation to each other. These scales focus on the relative differences or proportions between values rather than their absolute values.

This scale allows for classifying different elements into categories according to their size or intensity without the need to assign them exact numbers.

For example, the Likert scale presents a series of statements or items and asks respondents to indicate their level of agreement or disagreement with each statement. It typically ranges from “strongly agree” to “strongly disagree,” and respondents select the option that best represents their opinion on each statement. The Likert scale doesn’t measure an absolute quantity but rather the relative intensity or degree of agreement or disagreement with a statement.

### When is a scale relative?

A scale is considered relative when it measures or represents values based on their relationships or comparisons within a specific context or dataset rather than focusing on absolute values.

On a relative scale, the relationship between numbers and their meanings can vary depending on how the measurement categories are defined.

For example, the sizes “small”, “medium”, and “large” are not linked to any physical measure such as centimetres or feet; that is, there is no number assigned, but rather they refer to differences, or comparisons between values within a specific context or dataset, without solely focusing on their absolute measurements.

## Summary

Logarithmic price scales stand as invaluable tools in financial analysis, offering a unique perspective on price movements by combining a logarithmic price scale for percentage changes with a linear scale for absolute values.

In the realm of trading and investing, these charts provide a clearer visualisation of trends, patterns, and proportional shifts in asset prices over time.

## FAQs

### When should I use a semi-log chart?

Use a semi-log chart when analysing financial data that spans a wide range of values and has experienced significant percentage changes. It's particularly beneficial for visualising long-term trends, identifying support and resistance levels, and gaining insights into exponential price movements.

### Are there any limitations to using semi-log charts?

One limitation of semi-log charts is that they might not offer a precise representation of absolute values, as the focus is primarily on percentage changes. Additionally, interpreting data solely based on visual representation requires understanding the scale used and the potential distortion it might introduce, especially when comparing different timeframes or datasets.

### Are semi-log charts suitable for all types of financial analysis?

While semi-log charts are useful for analysing assets with significant percentage changes, they might not be ideal for all types of financial analysis. For instance, when focusing solely on short-term fluctuations or specific absolute price levels without emphasising percentage changes, other charting methods might be more suitable.

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