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**Logarithmic and Trigonometric Functions**

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**Logarithmic Function 104 = 10,000 10-1 = 0,1 = 1/10 103 = 1,000**

102 = 100 101 = 10 100 = 1 10-1 = 0,1 = 1/10 10-2 = 0,01 = 1/100 10-3 = 0,001 = 1/1000 10-4 = 0,0001 = 1/10000 10-5 = 0,00001 = 1/100000

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**Logarithmic Function Log10 10,000 (104) = 4 Log10 1,000 (103) = 3**

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The index of the log of any given number is one less than the number of figures before the decimal point in the given number. Log ,37 = 3, Log10 639,054 = 2, Log10 73,0956 = 1, Log10 5,65473 = 0,

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**If the index of the log is less than 1**

If the index of the log is less than 1. The number of figures is the how many number of zero the decimal point in the given number. Log10 0,87635 = - 1, Log10 0,02536 = - 2, Log10 0,00234 = - 3, Log10 0,00053 = - 4,

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**The index of the log is obtained in the given number**

The index of the log is obtained in the given number. Then find the matrix with using Norie’s Table. Log = 3,73062 Log10 537,8 = 2,73062 Log10 53,78 = 1,73062 Log10 5,378 = 0,73062 Log10 0,5378 = - 1,73062 Log10 0, = - 2,73062 Log10 0, = - 3,73062 Log10 0, = - 4,73062

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Example 1: Log 5794,5 = ? 3, = 3,76302 Log 5794,5 = 3,76298 + 4 = 3,76302

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Example 2: Log 5541,5 3,73572 = Log ? 3,73572 = 5441,5 = 4

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**The use of logs If a x b = c, then Log a + Log b = Log c**

3 x 4 = 12, then Log 3 + Log 4 = Log 12 3 x 4 = 12 Log 3 + Log 4 = Log 12 Log 3 = 0,47712 Log 4 = 0,60206 Log 12= 1,07918

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**The use of logs If a ÷ b = c, then Log a - Log b = Log c**

12 ÷ 3 = 4, then Log 12 - Log 3 = Log 4 12 ÷ 3 = 4 Log 12 - Log 3 = Log 4 Log 12= 1,07918 Log 3 = 0,47712 Log 4 = 0,60206

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**Trigonometric Function**

Logarithmics values might also be pointed out here that the logs sin, cos, tan, etc., of < A may be derived from their natural number, and we would learn the student to the explanation on how to use these Tables. (Norie’s Table) Log sin 10 38,7 = 8,45798 Log tan ,5 = 8,55205 Log cosec ,4 = 10,35702 Log sec ,3 = 10,04850 Log cot ,0 = 9,72354

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Example 3: Log sin ,8 = ? 9, = 9,70413 “+” ?

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Example 4: 9,70521 = sin ? Sin ,8 70521 – = 17

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**THIS PRESANTATION WAS PREPARED**

BY EVREN GÜREL E MAIL : : Mobile Phone : Phone :

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