Definition: Logarithmic inequality — inequality in which the variable is under the sign of logarithm.
So good to be able rozwiazywanie logarithmic inequality, you need to be able to control the reference ratio of the logarithm.
Equivalent transformation of simple logarithmic inequalities.
When the inequality sign does not change and accounted for DHS.
Examples of the solution of the simplest logarithmic equations
Since 5>1, the function is increasing and, given DHSreceived
Here it is
Since , the function is decreasing and, given DHSreceived
Here is rozvytku no.
Then that is
Answer: rozvytku no.
The scheme is more complex logarithmic equations
- Using method of intervals
- The use of equivalent transformations
As razvesti logarithmic equation
Using the formulae of logarithm and potentiating reduce the equation to a simple (consider the initial DHS and make sure not to lose roots when sujuan DHS). After transformation, if it is not possible to reduce to a simple logarithmic equations we are trying to introduce a change of variables.
Examples of the solution of logarithmic inequalities
Logarithmic inequality rozwadowska as well as the logarithmic equations.
Example 3 (use of formulas, logarithms)
Going to the base 2, we get the equivalent equation
Example 4 (using properties of logarithmic functions)
The function increases in scope as the sum of two increasing functions, and comes. Therefore, the given equation has a single root