Are Common Logarithms Explained in Your Textbook?

Thread starter Paulo2014
Start date Mar 21, 2008
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Logarithms

In summary, a common logarithm is a mathematical function that represents the power to which the number 10 must be raised to equal a given number. It is different from a natural logarithm, which uses the number e as its base. Common logarithms are useful for simplifying calculations and comparisons of very large or very small numbers, and can be used to solve equations involving logarithms by using the laws of logarithms and inverse operations. Common logarithms can also be negative when the given number is less than 1.

Mar 21, 2008

Paulo2014

what are common logarithms? my textbook doesn't explain it very well

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Mar 21, 2008

scarecrow

It's a logarithm with base 10.

http://en.wikipedia.org/wiki/Common_logarithm

Last edited: Mar 21, 2008

1. What is a common logarithm?

A common logarithm, also known as a base 10 logarithm, is a mathematical function that represents the power to which the number 10 must be raised to equal a given number. In other words, it is the inverse function of exponentiation with a base of 10.

2. How is a common logarithm different from a natural logarithm?

A natural logarithm, also known as a base e logarithm, uses the number e (approximately equal to 2.71828) as its base, while a common logarithm uses the number 10 as its base. This means that the natural logarithm is the inverse function of exponentiation with a base of e, while the common logarithm is the inverse function of exponentiation with a base of 10.

3. What is the purpose of using common logarithms?

Common logarithms are useful for simplifying calculations and comparisons of very large or very small numbers. They can also be used to convert between exponential and logarithmic functions, and are frequently used in scientific and engineering calculations.

4. How do you solve equations involving common logarithms?

To solve an equation involving common logarithms, you can use the laws of logarithms, such as the power rule and product rule, to simplify the expression. Then, you can isolate the variable by using inverse operations, such as exponentiating both sides to remove the logarithm.

5. Can common logarithms be negative?

Yes, common logarithms can be negative. This occurs when the given number is less than 1, as the power to which 10 must be raised to equal that number will be a negative value. For example, the common logarithm of 0.001 is -3, as 10 to the power of -3 equals 0.001.