Pokaznikiv-exponential equations

Definition: Pokaznikiv-exponential equation — an equation that contains the expression type , i.e. equations of the form

Main ways solution pokaznikiv-exponential equations and inequalities

For the case f(x)>0

Example 1

Solutions:

Answer:

Example 2

Solutions:

At DHS, both parts of the equation are positive, therefore, after taking the logarithm of base 10, we obtain the equation equivalent to this

Here

Replacement

Then or , ie (both the root lead to DHS)

Answer:

For the case f(x) — an arbitrary expression

Example 3

Solutions:

If you count the base number, then

1) the right to equality;

2) when properly;

3) when properly;

4) if that is true equality.

Answer:

Note: If count-based variable, the function is deemed to have arisen only when . From this point of view, this equation has only two roots: