Instruction

1

Turning to the study of inequalities with logarithms, you should be able to solve logarithmic equations know the properties

**of logarithms**, definition of a logarithm.2

The solution to all problems on logarithms start with the finding DHS - region of the allowed values. The expression under the logarithm must be positive, the base of the logarithm must be greater than zero and not equal to one. Follow rovnoselmash transformations. DHS at each step should remain the same.

3

When solving logarithmic inequalities, it is important that both sides of the sign were logarithms, and with the same base. If any parties are represented, the number, write it as a logarithm, by applying the definition of a logarithm. The number of b equals the number a to the power log, where log is the logarithm of b to base a. Basic logarithmic celebration is, in fact, the definition of the logarithm.

4

Solving logarithmic

**inequalities**, note the base of the logarithm. If it is greater than one, when you get rid**of the logarithms**, i.e. in the transition to simple numerical inequalities, the inequality sign remains the same. If the base of logarithm from zero to unity, the inequality sign is reversed.5

It is useful to remember the key properties

**of logarithms**. The logarithm of one is equal to zero, logarithm of a to base a is equal to one. The logarithm of product is sum**of logarithms**, the logarithm of the private equal to the difference**of the logarithms**. If podogretoe expression raised to the power B, it is possible to make it for the sign of the logarithm. If the base of the logarithm raised to the power A, the sign of the logarithm can be taken the number 1/A.6

If the base of the logarithm represented by some expression Q that contains the variable x, it is necessary to consider two cases: Q(x) ϵ (1;+∞) and Q(x) ϵ (0;1). Accordingly, it is a sign of inequality in the transition from a logarithmic to a simple algebraic comparison.