Common Logarithm Calculator

What is Common Logarithm?

A common logarithm, also known as the base-10 logarithm or decadic logarithm, is the logarithm to the base 10. It is denoted as log₁₀(x) or simply log(x). Common logarithms are widely used in various fields including science, engineering, and mathematics due to their convenience in working with decimal number systems.

How to Calculate Common Logarithm

To calculate the common logarithm of a number x, we need to find y such that 10^y = x. This is typically done using calculators, computers, or logarithm tables, as manual calculation can be complex for most numbers.

Formula

The formula for a common logarithm is:

\[ y = \log_{10}(x) \]

Which is equivalent to:

\[ 10^y = x \]

Where x is the number we're taking the logarithm of, and y is the result.

Calculation Steps

1. Identify the number x for which you want to calculate the common logarithm
2. Use a calculator or computational tool to evaluate log₁₀(x)
3. If using a scientific calculator, you can usually use the "log" button directly
4. If using a natural logarithm (ln) function, you can use the formula: log₁₀(x) = ln(x) / ln(10)
5. Verify your result by calculating 10^y, which should approximately equal x

Example

Let's calculate \(\log_{10}(100)\):

1. We want to find y such that \(10^y = 100\)
2. Using a calculator or by recognizing that \(10^2 = 100\), we find that \(\log_{10}(100) = 2\)
3. To verify: \(10^2 = 100\), which confirms our result

Therefore, \(\log_{10}(100) = 2\)

Graph of y = log₁₀(x) showing the point (100, 2)