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DOKUZ EYLUL UNIVERSITYDOKUZ EYLUL UNIVERSITYSCHOOL OF SCHOOL OF MARITIME BUSINESS AND MANAGEMENTMARITIME BUSINESS AND MANAGEMENT
DEPARTMENT OF DECKDEPARTMENT OF DECK
E.GürelE.Gürel
Logarithmic and Trigonometric Logarithmic and Trigonometric FunctionsFunctions
DOKUZ EYLUL UNIVERSITYDOKUZ EYLUL UNIVERSITYSCHOOL OF SCHOOL OF MARITIME BUSINESS AND MANAGEMENTMARITIME BUSINESS AND MANAGEMENT
DEPARTMENT OF DECKDEPARTMENT OF DECK
E.GürelE.Gürel
Logarithmic FunctionLogarithmic 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
DOKUZ EYLUL UNIVERSITYDOKUZ EYLUL UNIVERSITYSCHOOL OF SCHOOL OF MARITIME BUSINESS AND MANAGEMENTMARITIME BUSINESS AND MANAGEMENT
DEPARTMENT OF DECKDEPARTMENT OF DECK
E.GürelE.Gürel
Logarithmic FunctionLogarithmic 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
DOKUZ EYLUL UNIVERSITYDOKUZ EYLUL UNIVERSITYSCHOOL OF SCHOOL OF MARITIME BUSINESS AND MANAGEMENTMARITIME BUSINESS AND MANAGEMENT
DEPARTMENT OF DECKDEPARTMENT OF DECK
E.GürelE.Gürel
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,........
DOKUZ EYLUL UNIVERSITYDOKUZ EYLUL UNIVERSITYSCHOOL OF SCHOOL OF MARITIME BUSINESS AND MANAGEMENTMARITIME BUSINESS AND MANAGEMENT
DEPARTMENT OF DECKDEPARTMENT OF DECK
E.GürelE.Gürel
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,........
DOKUZ EYLUL UNIVERSITYDOKUZ EYLUL UNIVERSITYSCHOOL OF SCHOOL OF MARITIME BUSINESS AND MANAGEMENTMARITIME BUSINESS AND MANAGEMENT
DEPARTMENT OF DECKDEPARTMENT OF DECK
E.GürelE.Gürel
The index of the log is obtained in the given number. Then find the matrix with using Norie’s Table.
Log10 5378 = 3,73062Log10 537,8 = 2,73062Log10 53,78 = 1,73062Log10 5,378 = 0,73062
Log10 0,5378 = - 1,73062Log10 0,05378 = - 2,73062Log10 0,005378 = - 3,73062Log10 0,0005378 = - 4,73062
DOKUZ EYLUL UNIVERSITYDOKUZ EYLUL UNIVERSITYSCHOOL OF SCHOOL OF MARITIME BUSINESS AND MANAGEMENTMARITIME BUSINESS AND MANAGEMENT
DEPARTMENT OF DECKDEPARTMENT OF DECK
E.GürelE.Gürel
DOKUZ EYLUL UNIVERSITYDOKUZ EYLUL UNIVERSITYSCHOOL OF SCHOOL OF MARITIME BUSINESS AND MANAGEMENTMARITIME BUSINESS AND MANAGEMENT
DEPARTMENT OF DECKDEPARTMENT OF DECK
E.GürelE.Gürel
DOKUZ EYLUL UNIVERSITYDOKUZ EYLUL UNIVERSITYSCHOOL OF SCHOOL OF MARITIME BUSINESS AND MANAGEMENTMARITIME BUSINESS AND MANAGEMENT
DEPARTMENT OF DECKDEPARTMENT OF DECK
E.GürelE.Gürel
Example 1:Example 1:
Log 5794,5 = ?
Log 5794,5 = 3,76298
3,76298 + 4 = 3,76302
+ 4= 3,76302
DOKUZ EYLUL UNIVERSITYDOKUZ EYLUL UNIVERSITYSCHOOL OF SCHOOL OF MARITIME BUSINESS AND MANAGEMENTMARITIME BUSINESS AND MANAGEMENT
DEPARTMENT OF DECKDEPARTMENT OF DECK
E.GürelE.Gürel
Example 2:Example 2:
3,73572 = Log ?
3,73572 = 5441,5
Log 5541,5
73572 - 73568 = 4
DOKUZ EYLUL UNIVERSITYDOKUZ EYLUL UNIVERSITYSCHOOL OF SCHOOL OF MARITIME BUSINESS AND MANAGEMENTMARITIME BUSINESS AND MANAGEMENT
DEPARTMENT OF DECKDEPARTMENT OF DECK
E.GürelE.Gürel
The use of logsThe 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
DOKUZ EYLUL UNIVERSITYDOKUZ EYLUL UNIVERSITYSCHOOL OF SCHOOL OF MARITIME BUSINESS AND MANAGEMENTMARITIME BUSINESS AND MANAGEMENT
DEPARTMENT OF DECKDEPARTMENT OF DECK
E.GürelE.Gürel
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
The use of logsThe use of logs
DOKUZ EYLUL UNIVERSITYDOKUZ EYLUL UNIVERSITYSCHOOL OF SCHOOL OF MARITIME BUSINESS AND MANAGEMENTMARITIME BUSINESS AND MANAGEMENT
DEPARTMENT OF DECKDEPARTMENT OF DECK
E.GürelE.Gürel
Trigonometric FunctionTrigonometric 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 = 8,45798Log tan 1770 57,5 = 8,55205Log cosec 260 04,4 = 10,35702Log sec 3330 25,3 = 10,04850Log cot 1170 53,0 = 9,72354
DOKUZ EYLUL UNIVERSITYDOKUZ EYLUL UNIVERSITYSCHOOL OF SCHOOL OF MARITIME BUSINESS AND MANAGEMENTMARITIME BUSINESS AND MANAGEMENT
DEPARTMENT OF DECKDEPARTMENT OF DECK
E.GürelE.Gürel
DOKUZ EYLUL UNIVERSITYDOKUZ EYLUL UNIVERSITYSCHOOL OF SCHOOL OF MARITIME BUSINESS AND MANAGEMENTMARITIME BUSINESS AND MANAGEMENT
DEPARTMENT OF DECKDEPARTMENT OF DECK
E.GürelE.Gürel
DOKUZ EYLUL UNIVERSITYDOKUZ EYLUL UNIVERSITYSCHOOL OF SCHOOL OF MARITIME BUSINESS AND MANAGEMENTMARITIME BUSINESS AND MANAGEMENT
DEPARTMENT OF DECKDEPARTMENT OF DECK
E.GürelE.Gürel
DOKUZ EYLUL UNIVERSITYDOKUZ EYLUL UNIVERSITYSCHOOL OF SCHOOL OF MARITIME BUSINESS AND MANAGEMENTMARITIME BUSINESS AND MANAGEMENT
DEPARTMENT OF DECKDEPARTMENT OF DECK
E.GürelE.Gürel
DOKUZ EYLUL UNIVERSITYDOKUZ EYLUL UNIVERSITYSCHOOL OF SCHOOL OF MARITIME BUSINESS AND MANAGEMENTMARITIME BUSINESS AND MANAGEMENT
DEPARTMENT OF DECKDEPARTMENT OF DECK
E.GürelE.Gürel
Example 3:Example 3:
Log sin 300 23,8 = ?
9,70396 + 17 = 9,70413
“+” ?
DOKUZ EYLUL UNIVERSITYDOKUZ EYLUL UNIVERSITYSCHOOL OF SCHOOL OF MARITIME BUSINESS AND MANAGEMENTMARITIME BUSINESS AND MANAGEMENT
DEPARTMENT OF DECKDEPARTMENT OF DECK
E.GürelE.Gürel
Example 4:Example 4:
9,70521 = sin ?
Sin 300 28,8
70521 – 70504 = 17
DOKUZ EYLUL UNIVERSITYDOKUZ EYLUL UNIVERSITYSCHOOL OF SCHOOL OF MARITIME BUSINESS AND MANAGEMENTMARITIME BUSINESS AND MANAGEMENT
DEPARTMENT OF DECKDEPARTMENT OF DECK
E.GürelE.Gürel
THIS PRESANTATION WAS PREPARED THIS PRESANTATION WAS PREPARED BY EVREN GÜRELBY EVREN GÜREL
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