Decimal logarithms which it is accepted to call standard are most often put into practice. For their location are made special tables, using which it is possible to find value of a logarithm of any positive number with any given accuracy, previously having led it to a standard look. Four-digit tables of Bradis to within 0.0001 which contain mantissas of decimal logarithms are quite sufficient for the solution of the majority of tasks. Characteristic can be found easily by one type of number. The address with tables very simple.
It is required to you
- - transition formula from one basis of a logarithm to another;
- - four-digit mathematical tables of Bradis.
Instruction
1. Lead a logarithm to a standard look if its basis is not equal to 10. Use a transition formula from one basis to another.
2. Find characteristic of a logarithm. If the number is more or equally to unit, then count the number of figures in the whole part of this number. Take away unit from this quantity and receive value of characteristic. For example, at number 56.3 logarithm the characteristic is equal to 1. If the number is decimal fraction, smaller 1, then count in it the number of zero to the first figure other than zero. Make negative the learned value of characteristic. For example, at number 0.0002 logarithm the characteristic is equal to-4.
3. Define number for finding of a mantissa as whole. Ignore a comma if it is in this number and reject all zero standing at the end of number. The provision of a comma in decimal number and the last zero in no way do not influence mantissa size. Write down the formed integer. For example, at number 56.3 logarithm it is equal to 563. Depending on that how many figures contain in this number, the operation algorithm with four-digit tables depends. There are three types of algorithms.
4. Find a logarithm mantissa, having performed the following operations if the number for its location is three-digit. Find table XIII "Mantissas of decimal logarithms" in four-digit mathematical tables of Bradis. Pass to the line containing these two first figures of number on which the mantissa is looked for in the first N column. For example, if we have number 563, then look for a line where in the first column costs 56. Then move ahead on this line before its crossing to the right with a column which number coincides with the third figure of initial number. In our example it is a column with number 3. On crossing of the found line and column there is a value of a mantissa. The mantissa found on number 563 is equal to 0.7505.
5. Find a logarithm mantissa, having performed the following operations if the number for its location consists of two or one figures. Attribute mentally to this number such number of zero that it became three-digit. If the number is equal 56, then 560 turn out. Find a mantissa on the received three-digit number. For this purpose perform operations from a step 4. The mantissa on number 560 is equal to 0.7482.
6. Find a logarithm mantissa, having performed the following operations if the number for its location is four-digit. Find a mantissa for the number represented by the first three figures of this number. For this purpose perform operations from a step 4. Then move on a horizontal line from the found mantissa in the right part of the table located behind vertical fat line and the containing amendment on the fourth figure. Find in area of amendments a column with number coinciding with the fourth figure of number. Add the amendment which is on crossing of a line and column to the mantissa found on three-digit number. For example, if the number for finding of a mantissa is equal 5634, then the mantissa on 563 is equal to 0.7505. The amendment on figure 4 is equal to 3. The final result is equal to 0.7508.
7. Find a logarithm mantissa, having performed the following operations if the number for it contains more than four figures. Round number to four signs so that all figures, starting with the fifth, were zero. Reject the last zero and find a mantissa on four-digit number. For this purpose perform operations from a step 7.
8. Find a number logarithm as the sum of characteristic and a mantissa. The logarithm of number 56.3 is equal in the reviewed example to 1.7505.