Log Formulas

About Log Formulas

Let us first define logs before studying log formulas (logarithms). Exponents are written in a logarithmic format. We employ logarithms when we can't solve an issue using exponents. The rules of exponents can be used to derive a variety of logarithm formulas.

What do you mean by Log Formulas?

Let's deal with a few things before we go into the log formulas. There are two forms of logarithms: common logarithms (written as "log") and natural logarithms (whose base is 10 if not specified) (which is written as "ln" and its base is always "e"). For common logarithms, the formulas are presented below. They are, nevertheless, all relevant to natural logarithms.

Some of these laws have special names, such as the product formula of logs, which is log_b (xy) = log_b x + log_b y.

Similarly, all of the properties are listed here, along with their names.

Product Formula of logarithms

The product formula of logs is, log_b(xy) = log_b x + log_b y.

Quotient Formula of logarithms

The quotient formula of logs is, log_b (x/y) = log_b x - log_b y.

Power Formula of Logarithms

The power formula of logarithms says log_b ax = x log_b a.

Change of Base Formula of Logarithms

The change of base formula of logs says log_b a = (log_b a) / (log_b b).

Types of Logarithms

There are several types of logarithms, depending on the base:

1. Common Logarithms: The common logarithm has a base of 10. It is denoted as log⁡(x)\log(x)log(x) or log⁡10(x)\log_{10}(x)log10​(x). These logarithms are widely used in scientific calculations, especially in dealing with large or small numbers.

2. Natural Logarithms: The natural logarithm has a base of eee (Euler's number), approximately equal to 2.718. It is denoted as ln⁡(x)\ln(x)ln(x). Natural logarithms are prevalent in calculus, particularly in solving problems related to growth and decay, and in the analysis of continuous processes.

3. Binary Logarithms: The binary logarithm has a base of 2, denoted as log⁡2(x)\log_2(x)log2​(x). This is commonly used in computer science, particularly in algorithms and information theory, where quantities are expressed in powers of 2.

There are several types of logarithms, depending on the base:

1. Common Logarithms: The common logarithm has a base of 10. It is denoted as log⁡(x)\log(x)log(x) or log⁡10(x)\log_{10}(x)log10​(x). These logarithms are widely used in scientific calculations, especially in dealing with large or small numbers.

2. Natural Logarithms: The natural logarithm has a base of eee (Euler's number), approximately equal to 2.718. It is denoted as ln⁡(x)\ln(x)ln(x). Natural logarithms are prevalent in calculus, particularly in solving problems related to growth and decay, and in the analysis of continuous processes.

3. Binary Logarithms: The binary logarithm has a base of 2, denoted as log⁡2(x)\log_2(x)log2​(x). This is commonly used in computer science, particularly in algorithms and information theory, where quantities are expressed in powers of 2.

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