Exponential inequalities

Equivalent transformation of simple inequalities

When a > 1

The inequality sign is preserved.

Example 1

Rozwarte inequality:

Solutions:

A function is increasing, therefore equate indices,

Answer:

If 0 < a < 1

The inequality sign is reversed.

Example 2

Rozwarte inequality:

Solutions:

Function y=0,7^t~ is decreasing, therefore equate indices,

Answer:

More complex exponential inequalities

With the help of equivalent transformations

With the help of equivalent transformations (scheme the solution of model equations) given inequality reduces to the known inequality of the form (square, fractional or other). After the solution of the resulting inequality we come to the simplest exponential inequalities.

Example 3

Rozwarte inequality:

Solutions:

Substitution gives the inequality

junctions which or

So

(rozvytku no), or where that is

Answer:

Using the General method of intervals

Apply the General method of intervals,

  1. Find odz
  2. Find the zeros of the function
  3. Mark the zeros of the function at DHS and find the sign in each of the intervals to which DHS is broken.
  4. Write down the answer, given the inequality sign.

Example 4

Rozwarte inequality:

Solutions:

Solve the inequality by the method of intervals. The given inequality weselna bumps

We denote

  1. DHS:
  2. The zeros of the function:
  3. Because the function is increasing, the value of zero, it takes only one point of the region definition:
  4. Denote the zero function on DHS, find the sign in each of the intervals to which DHS Rotblat, and record the interchange of bumps

Answer:

The solution to inequalities is very similar to the model equations, so if You haven't found a suitable Roseanna irregularities, see exponential equations.

Chapter:
Versions in other languages: