#### Table of Contents

#### Introduction

Logarithms are confusing! This blog explains what logarithms are, how they are used, and gives two easy equations to convert between decibels and linear units.

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#### What's a Base?

A number can be represented by a base raised to an exponent. For example, the number 100 can be written as

(1)

The number 10 is the base and the exponent is 2. Here are more examples:

(2)

(3)

The base can be changed to other numbers. For example, base 2:

(4)

(5)

The base can also be Euler’s number e,

(6)

(7)

#### Why Logarithms?

The base of a logarithm is written as a subscript. For example, a base 10 logarithm is written as , a base 2 logarithm is written as , and a natural logarithm may be written as or .

Logarithms are used to represent numbers by their exponent. Logarithms act as if a number is represented by a base raised to an exponent, and then they calculate that exponent.

(8)

(9)

(10)

(11)

#### Linear to Decibels

#### Conclusion

Numbers can be represented by a base number raised to an exponent. Logarithms are useful in representing the exponents of base numbers. Engineers use 10log10() to convert linear units into decibels.

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