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Logarithmic and Trigonometric Functions

Logarithmic and Trigonometric Functions. Logarithmic Function. 10 4 = 10,000 10 3 = 1,000 10 2 = 100 10 1 = 10 10 0 = 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. Logarithmic Function.

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Logarithmic and Trigonometric Functions

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  1. Logarithmic and Trigonometric Functions

  2. Logarithmic Function 104 = 10,000 103 = 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

  3. Logarithmic Function Log10 10,000 (104) = 4 Log10 1,000 (103) = 3 Log10 100 (102) = 2 Log10 10 (101) = 1 Log10 0,1 (10-1) = -1 Log10 0,01 (10-2) = -2 Log10 0,001 (10-3) = -3 Log10 0,0001 (10-4) = -4 Log10 1 = 0

  4. 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. Log10 4865,37 = 3,........ Log10 639,054 = 2,........ Log10 73,0956 = 1,........ Log10 5,65473 = 0,........

  5. 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,........

  6. The index of the log is obtained in the given number. Then find the matrix with using Norie’s Table. Log10 5378 = 3,73062 Log10 537,8 = 2,73062 Log10 53,78 = 1,73062 Log10 5,378 = 0,73062 Log10 0,5378 = - 1,73062 Log10 0,05378 = - 2,73062 Log10 0,005378 = - 3,73062 Log10 0,0005378 = - 4,73062

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

  8. Example 2: Log 5541,5 3,73572 = Log ? 3,73572 = 5441,5 73572 - 73568 = 4

  9. 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

  10. 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

  11. 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 1770 57,5 = 8,55205 Log cosec 260 04,4 = 10,35702 Log sec 3330 25,3 = 10,04850 Log cot 1170 53,0 = 9,72354

  12. Example 3: Log sin 300 23,8 = ? 9,70396 + 17 = 9,70413 “+” ?

  13. Example 4: 9,70521 = sin ? Sin 300 28,8 70521 – 70504 = 17

  14. THIS PRESANTATION WAS PREPARED BY EVREN GÜREL E MAIL : e.gurel@deu.edu.tr : evrengurel@mynet.com.tr Mobile Phone : 0 532 427 38 17 Phone : 0 232 329 47 02

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