**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: