Показательные и логарифмические уравнения и неравенства.
Equations of the form af (x) = b, a > 0, a ≠ 1, b > 0
By definition of logarithm from the main logarithmic identity, we get that If f (x) is an algebraic function, then this equation will be algebraic, which can be solved using standard techniques (as is a specific number that is the same as 5, π, etc.).
Equations of the form
These equations are solved in two stages:
a) by replacing this equation reduces to the equation F (t) = 0, which finds all the positive roots (though the roots of such pstoc exactly).
b) For each solved equation of the type discussed above:
These two types of model equations are essential to them are all the other methods.
Logarithmic equations
Equations of the form loga f (x) = b, a > 0, a ≠ 1
Here it is assumed that f (x) be a function equation which we already know how to solve it. By definition of the logarithm of the basic logarithmic identities get чтоf (x) = ab. This equation can be solved by any available methods, since ab is a number.
Equations of the form
Quite similarly exponential equations, equations of this type are solved in two stages.
• By replacing this equation reduces to the equation F (x) = 0, which finds all the roots (even if such roots are exactly n pieces).
• Each solves the equation of the type discussed above:
It is clear that it is not necessary equation will be considered. So, in the process of transformation of the logarithmic equations, the aim should be to bring all members of the equation logarithms to one base. It is necessary to remember about the field of definition of the considered expressions, trying to transform it did not go down those roots, which may be purchased, it will be possible to weed out the check.
The inequality is two numbers or mathematical expressions connected by one of the characters: (more) (less) (more or equal), (less or equal). The entry has the same meaning, so that the presence of two opposite signs of the inequality is simply an additional convenience. Inequalities that contain an or, called strict, and contain an or – lax
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