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A logarithm is the power to which a number must be raised in order to get some other number (see Section 3 of this Math Review for more about exponents). For example, the base ten logarithms of 100 is 2, because ten raised to the power of two is 100: log 100 = 2. Because. 102 = 100.
The logarithm, or log, is the inverse of the mathematical operation of exponentiation. This means that the log of a number is the number that a fixed base has to be raised to in order to yield the number. Conventionally, log implies that base 10 is being used, though the base can technically be anything.
0:07 2:11 Suggested clip How to Calculate Log (Easy) — YouTubeYouTubeStart of suggested client of suggested clip How to Calculate Log (Easy) — YouTube
Logarithms are a convenient way to express large numbers. (The base-10 logarithm of a number is roughly the number of digits in that number, for example.) Slide rules work because adding and subtracting logarithms is equivalent to multiplication and division. (This benefit is slightly less important today.)
Multiply two numbers by adding their powers. For example: 102 × 103 = 105, or 100 × 1000 = 100,000. The natural log, represented by “LN”, is the base-e log, where e is the constant 2.718. This is a useful number in many areas of math and physics.
The natural logarithm function LN(x) is defined only for x>0. So the natural logarithm of a negative number is undefined. Ln(x) is undefined for x 0. The complex logarithmic function Log(z) is defined for negative numbers too.
2:05 8:04 Suggested clip How to Understand Logarithms: the Basics — YouTubeYouTubeStart of suggested client of suggested clip How to Understand Logarithms: the Basics — YouTube
16:11 19:15 Suggested clip Logarithms How? (Nancy) — YouTubeYouTubeStart of suggested client of suggested clip Logarithms How? (Nancy) — YouTube
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