Logarithmic equations

Definition: Logarithmic equation — an equation in which the variable is under the sign of logarithm..

So good to be able rozwiazywanie logarithmic equations, you need to be able to control the reference ratio of the logarithm.

Equivalent transformation of simple logarithmic equations.

Since the DHS and therefore the initial equation is automatically taken into account.

or

Examples of the solution of the simplest logarithmic equations

Example 1

Rozwarte equation:

Solutions:

Answer:

Example 2

Rozwarte equation:

Solutions:

(DHS also considered)

Then that is

Answer:

The scheme is more complex logarithmic equations

  1. The use of equations and effect
  2. Using the properties of the relevant functions
  3. 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 equations

Example 3 (use of formulas, logarithms)

Rozwarte equation:

Solutions:

Going to the base 2, we get the equivalent equation

Replacement

Then

Answer:

Example 4 (using properties of logarithmic functions)

Rozwarte equation:

Solutions:

The function increases in scope as the sum of two increasing functions, and comes. Therefore, the given equation has a single root

Answer:

Chapter:
Versions in other languages: