Contoh Soal Log atematika dalam Bahasa Inggris + Materi AntiLogaritma

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Example 1.16

1.    Solve the following logarithms (numbers greater than 10). a. log 53.2          1 b. log 234,000

2.    Solve the following logarithms (numbers between 0 and 1). a. log 0.532       b. log 0.00532

Answer :

1.       a. log 53.2 = log (5.32 x 10')                                   b. log 234,000 = log (2.34 x 105)

= log 5.32 + log 10'                                         = log 2.34 + log 105

= 0.726 + 1                                                    = 0.369 + 5

= 1.726                                              = 5.369

2.    a. log 0.532                           = log 5.32 x 10' = log 5.32 – 1 = 0.726 – 1 = –0.274

b. log 0.00532 = log 5.32 x ₁₀-3 = log 5.32 – 3 = 0.726 – 3 = –2.274

5. Determining Antilogarithm of a Number

 After learning about the ways to determine the logarithm of a number, now you will be introduced to the concept of the antilogarithm ofa number, which is an inverse of the logarithm. Determining the antilogarithm ofa number means finding a number which is given its logarithm value using antilogarithm table. To determine antilogarithm of a number, study the following examples.

Table 1.2 Antilogarithm Table

X	0	1	2	3	4	5	6	7	8	9
00	100	100	101	101	100	101	101	102	102	102
01	102	103	103	103	103	104	104	104	104	104
02	105	105	105	105	106	106	106	106	107	107
03	107	107	108	108	108	108	109	109	109	109
04	110	110	110	110	111	111	111	111	112	112
05	112	112	113	113	113	114	114	114	114	115
06	115	115	115	116	116	116	116	117	117	117
07	117	118	118	118	119	119	119	119	120	120
08	120	121	121	121	121	122	122	122	122	123
09	123	123	124	124	124	124	125	125	125	126
10	126	126	126	127	127	127	128	128	128	129
11	129	, 129	129	130	130	130	131	131	131	132
12	132	132	132	133	133	133	134	134	134	135

Determine the numbers which satisfy the following logarithms! a. 0.125                         b. 1.412

Answers:

a. Antilog 0.125 = 1.33

From the antilogarithm table, find the two first decimals in the most left column (column x), that is 12, then draw a line horizontally from that number to the right until intersect the column' which indicates number 5, so you obtain 133.

Because the integer (characteristic) is 0, thus the antilog 0.125 = 1.33

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