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Although a four-place log table is used here,
for purposes where accuracy to 3 significant
figures is required, generally, a three place
table is sufficiently accurate for all practical
purposes. Since the mantissa of a logarithm
represents only the significant figures of any
number, the same mantissa is used for 0.04,
4,400, etc., the decimal point being fixed
later by the characteristic. Therefore any
number consisting of 1 or 2 significant fig-
ures, may be found in the column marked
N, and its mantissa will be found on the
same line in this column headed by 0. For
any number containing 3 significant figures,
locate the first two figures in the N column,
and the third figure in the column headed
by the coresponding digit. The mantissa
will be found in this column, on a line even
with the first two digits.
|0.15||1.5||*||10-1||-1 or 9 - 10|
|0.015||1.5||*||10-2||-2 or 8 - 10|
|0.0015||1.5||*||10-3||-3 or 7 - 10|
Therefore, to find the logarithm of any
Write the number as a power of 10,
and put down the resulting exponent
of 10 as thecharacteristic.
determine the mantissa from the log
tables on page 102, and write this as a
decimal figure following the characteristic.
If the resulting logarithm has a negative char-
acteristic, change this to the positive form.
|Example: Find the logarithm of 0.00623:||log||21||=||1.3222|
Since 0.00623 = 6.23 * 10-3, The
acteristic is -3. The mantissa as
shown by the log table is 7945. The
resultant logarithm = 3.7945 or
when written in its positive form,
7.7945 - 10.
|log||0.0021||=||7.3222 - 10|
|log||0.0213||=||8.3284 - 10|
To find the log of any number having more
than three significant figures (by interpolation):
|1||:||Determine the characteristic.||log||0.003||=||7.4771 - 10|
Find the mantissa corresponding to
the first three significant figures.
The number corresponding to a given
logarithm is called the antilogarithm, and
is written "antilog". Example: Since log
of 692 = 2.8401, the antilog of 2.8401 = 692.
Finding the antilog of a number is the
reverse of finding the logarithm. First
locate the mantissa in the log table, and
determine its corresponding number. Now,
place the decimal as indicated by the char-
Find the next higher mantissa and
take the tabular difference.
Find the product of the tabular dif-
ference and the digit following the
first three significant figures of the
given number written as a decimal.
|5||:||Add this product to the lesser mantissa.|
|Example: Find the logarithm of 54.65.||
Example: To find the antilog of 3.9138,
look up 9138 in the log table. Its corre-
sponding number is 82, or expressed as a
power of 10, equals 8.2. A characteristic of
3 means that 8.2 must be multiplied by 10
Therefore, sntilog 3.9138 = 8.2 * 103 =
Since 54.65 = 5.465 * 101, the char-
acteristic is 1.
Next higher mantissa
Next lower mantissa
|Product||=||0.00040||Antilog||5.9138||=||8.2 * 105 = 820,000|
|Plus lesser mantissa||0.7372||Antilog||0.9138||=||8.2 * 100 = 8.2|
|Mantissa of 5.465||=||0.7376||Antilog||7.9138 - 10||=||8.2 * 10-3 = 0.0082|
|=||1.7376||Antilog||9.9138 - 10||=||8.2 * 10-1 = 0.82|
|To find the antilogarithm of a logarithm|
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