The Laws of Logs - Del Mar College

... 1. Log2 8 means 2 to the “what exponent” would give you 8, in other words, 2? = 8. So the exponent must be 3. Therefore, log2 8 = 3 since 23 = 8. 2. Log of base 10 (log10) is normally written without the 10; so for example, log 100 = log10 100. This is asking 10 to the “what exponent” would give you ...

... 1. Log2 8 means 2 to the “what exponent” would give you 8, in other words, 2? = 8. So the exponent must be 3. Therefore, log2 8 = 3 since 23 = 8. 2. Log of base 10 (log10) is normally written without the 10; so for example, log 100 = log10 100. This is asking 10 to the “what exponent” would give you ...

Section 10.3 3. a. log(1000)=3because1000=103 b. log(10

... exercise for future courses. See Example 8 on page 407 for a similar problem. .5 = .9i From the definition of the common logarithm on page 404 of the text, x may be written as ...

... exercise for future courses. See Example 8 on page 407 for a similar problem. .5 = .9i From the definition of the common logarithm on page 404 of the text, x may be written as ...

A First Digit Theorem for Square-Free Integer Powers

... We study the distribution of first digits of square-free integer powers. The method consists to fit the GBL to samples of first digits using two size-dependent goodness-of-fit measures, namely the ETA measure (derived from the mean absolute deviation) and the WLS measure (weighted least square measu ...

... We study the distribution of first digits of square-free integer powers. The method consists to fit the GBL to samples of first digits using two size-dependent goodness-of-fit measures, namely the ETA measure (derived from the mean absolute deviation) and the WLS measure (weighted least square measu ...

Aspectual Principle, Benford`s Law and Russell`s

... barber." Once in a small town a barber declared that he would shave everyone who did not shave himself. In so doing he boasted that he has no equal as for hairdressing but once he thought whether he should shave himself. On the one hand he should not do this because he shaves only others. But if he ...

... barber." Once in a small town a barber declared that he would shave everyone who did not shave himself. In so doing he boasted that he has no equal as for hairdressing but once he thought whether he should shave himself. On the one hand he should not do this because he shaves only others. But if he ...

# Benford's law

Benford's law, also called the First-Digit Law, is a phenomenological law about the frequency distribution of leading digits in many (but not all) real-life sets of numerical data. That law states that in many naturally occurring collections of numbers the small digits occur disproportionately often as leading significant digits. For example, in sets which obey the law the number 1 would appear as the most significant digit about 30% of the time, while larger digits would occur in that position less frequently: 9 would appear less than 5% of the time. If all digits were distributed uniformly, they would each occur about 11.1% of the time. Benford's law also concerns the expected distribution for digits beyond the first, which approach a uniform distribution.It has been shown that this result applies to a wide variety of data sets, including electricity bills, street addresses, stock prices, population numbers, death rates, lengths of rivers, physical and mathematical constants, and processes described by power laws (which are very common in nature). It tends to be most accurate when values are distributed across multiple orders of magnitude.The graph here shows Benford's law for base 10. There is a generalization of the law to numbers expressed in other bases (for example, base 16), and also a generalization from leading 1 digit to leading n digits.It is named after physicist Frank Benford, who stated it in 1938,although it had been previously stated by Simon Newcomb in 1881.