Logarithm (from Greek logos - "word", "relation", arithmos - "number") numbers b on the basis of a call an exponent in which it is necessary to build a to receive b. The antilogarithm is a function, the return logarithmic. The concept of an antilogarithm is used in engineering microcalculators and tables of logarithms.
It is required to you
- - table of antilogarithms;
- - engineering microcalculator.
Instruction
1. If you were given a logarithm x on a basis where x – the variable, then an antilogarithm for this function will be an exponential function of a^x. The exponential function has it name because unknown size x costs in an exponent.
2. Let, for example, y=log(2)x. Then y '=2^x antilogarithm. The natural logarithm of lnA will turn into the exponential e^A function as the exhibitor of e is the basis of a natural logarithm. The antilogarithm for a decimal logarithm of lgB has an appearance 10^B since number 10 is the basis of a decimal logarithm.
3. Generally, to receive an antilogarithm, build the logarithm basis in extent of podlogarifmenny expression. If variable x costs in the basis, then the power function will be an antilogarithm. For example, y=log(x)10 will address in y '=x^10. The power function is called so for the reason that the argument x is entered into a certain degree.
4. To find an antilogarithm of a natural logarithm on the engineering microcalculator, press on it ""shift"" or ""inverse"". Then press the ln button and enter value from which you want to take an antilogarithm. In some calculators it is required to press ""ln"" after input of number, and in some both options are equally possible.
5. For natural antilogarithms of e^x there is a special table. In it a certain range of values x is presented. As a rule, it covers number from 0.00 to 3.99. If degree is beyond this range, spread out it to such composed, for each of which the antilogarithm is known. Apply that property that e^(a+b)= (e^a) · (e^b).
6. In the left column the tenth shares of number are set. In "cap" from above – the 100-th. Let, for example, it is necessary to find e^1.06. Find line 1.0 in the left column. Find a column for 6 in the top line. On crossing of a line and column there is a cell 2.8864 which reports value for e^1.06.
7. To find e^4, present number 4 as the sum 3.99 and 0.01. Then e^4=e^ (3.99+0.01) =e^3,99·e^0,01=54,055·1,0101≈54,601 if to round result to three significant figures after a comma. By the way, if to consider 4=2+2, then about 54.599 will turn out. It is easy to notice that when rounding to two significant figures of number will coincide. In general, without errors it is not necessary to speak about exact number here as number e – is irrational.