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Inhaltsangabe: This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1896 Excerpt: ...J, fr, V 4. Find the value of log2 8, log2.6, logi 243, log5.04, logio 1000, logio.001. 5. Find the value of log. a1 logs Vb logs 2, logS7 3, logoo 10. y6. Prove that logCvx VT-. /9)= £log2 + log 7-flog 3. 121. That system of logarithms whose base is Io is called the common system of logarithms. In speaking of logarithms hereafter, common logarithms are referred to unless the contrary is expressly stated. We shall assume that an index of 10 can be found such that 10 affected with this index is practically equivalent to any number. The indices of these powers of 10, i.e. the common logarithms, are in general incommensurable numbers. Now, the greater the index with which 10 is affected, the greater will be the value of the equivalent expression; and the less the index, the less will be the numerical value of the expression. Hence, if one number be less than another, the logarithm of the first will be less than the logarithm of the second. But the student should notice that logarithms (or indices) are not proportional to the corresponding numbers. Example. 1000 is less than 10000; and the logarithm to base 10 of the first is 3 and of the second is 4. But 1000, 10000, 3, 4 are not in proportion. 122. Proposition. Iftwo numbers expressed in the decimal notation have the same digits arranged in the same order (so that they differ only in the position of the decimal point), their logarithms to the base 10 differ only by an integer. The decimal point in a number is moved by multiplying or dividing the number by some power of 10. Let the numbers be m and n; then m = n x 10 when A; is a whole number (positive or negative); then log m = log (n x 10) = log n + log 10 = log n + k. (Art. 120.) That is, logm and log?i differ by an integer. Q.e.d. Example 1. log 1679....

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## 1.Trigonometry for beginners

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ISBN 10: 1231331062 ISBN 13: 9781231331064
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