The logarithm of number b defines an exponent for construction of the initial positive number a which is the logarithm basis and receiving as a result of the set number b. The solution of a logarithm consists in definition of this degree on the set numbers. There are several basic rules for definition of a logarithm or transformation of record of logarithmic expression. Applying these rules and definitions it is possible to calculate the logarithmic equations, to find derivatives, to solve integrals and other expressions. The solution of a logarithm often looks as the simplified logarithmic record.
Instruction
1. Write down the set logarithmic expression. If in expression the logarithm on the basis 10 is used, then its record is shortened and looks so: lg b is a decimal logarithm. If the logarithm has in the form of the basis natural number e, then write down expression: ln b is a natural logarithm. It is meant that degree in which it is necessary to build basis number that number b turned out is result of any logarithm.
2. The solution of a logarithm consists in calculation of this degree. Before the decision the logarithmic expression, as a rule, is required to be simplified. Transform it, using the known identities, rules and properties of a logarithm.
3. Addition and subtraction of logarithms of numbers b and with on the identical bases is replaced with one logarithm with the work or division of numbers b and with respectively. Apply as necessary the most widespread transformation – a formula of transition of a logarithm to other basis.
4. Using expressions for simplification of a logarithm, consider the existing restrictions. So the basis of a logarithm and can be only positive number not equal to unit. Number b also has to be more than zero.
5. However not always, having simplified expression, it is possible to calculate a logarithm in its numerical look. Sometimes it does not make sense as many degrees represent irrational numbers. In that case leave degree of number written down in the form of a logarithm.