# how to use barcode in c#.net If we say that the natural logarithm of a certain number p is equal to q, what do we mean in Software Creation QR Code in Software If we say that the natural logarithm of a certain number p is equal to q, what do we mean

If we say that the natural logarithm of a certain number p is equal to q, what do we mean
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The natural logarithm (or natural log) of a number is the power to which we must raise Euler s constant, e, to get that number If we say that the natural log of p is equal to q, we mean p = eq The common log is sometimes called the base-e log, because e is the base that we raise to various powers The value of e is approximately 271828 It s an irrational number, however, so it cannot be fully written out in decimal form
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Question 29-5
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According to the definition in Answer 29-4, what is the natural log of e Of e 2 Of e 3 Of e4 What happens to the natural log of a number as that number grows larger without limit
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The natural log is related to a growing number like this: The natural log of e is 1, because e 1 = e The natural log of e 2 is 2 The natural log of e 3 3 The natural log of e 4 is 4
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As a number gets larger without limit, so does its natural log, but the size of the log grows much more slowly than the size of the number
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According to the definition in Answer 29-4, What is the natural log of 1 Of 1/e Of 1/e 2 Of 1/e 3 What happens to the natural log of a positive real number whose absolute value keeps shrinking What happens to the natural log of a shrinking positive real number when it actually becomes 0
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As the absolute value of a positive number keeps shrinking, its natural log changes like this: The natural log of 1 is 0, because e 0 = 1 The natural log of 1/e is 1 The natural log of 1/e 2 is 2 The natural log of 1/e 3 is 3
As a positive number approaches 0, its natural log becomes more negative There is no limit to how large negatively the log can get When the shrinking positive number actually reaches 0, its natural log is no longer defined in the set of real numbers (Perhaps it s non-real but complex, or maybe it s some other kind of number entirely Evaluating it is beyond the scope of this book)
Question 29-7
How can logarithms be used to change products into sums, or ratios into differences Do these properties of logs depend on the base
The logarithm of the product of two numbers is equal to the sum of their logarithms The logarithm of the ratio of two numbers is equal to the difference between their logarithms These rules work for common logs as well as for natural logs In fact, they work no matter what the base happens to be, as long as we don t change the base during the calculation!
Question 29-8
What is the common exponential of a number What is the natural exponential of a number