The equation, in which the unknown is in the degree index (at least to one degree), is called **an exponential equation**.

There is no general method for solving an exponential equation.

**Solve some types of exponential equations**

**1) Solve an equation of type**

**aₓ = **b, (a> 0, a ≠ 1)

If** b> 0,** then the equation has a unique solution

*х = logₐ b*

If ** b ≤ 0, **the equation has no solution.

**2) Solve the water equation**

This equation at ** a> 0 a**nd

**is equivalent to the equation**

*a ≠ 1*

**f (x) = ψ (x**).**Example.**

**3) Solve the equation of sight**

When

* a> 0, a ≠ 1; b> 0, b ≠ 1, a *f

*d*

**(x) an****are given algebraic functions, by logarithmizing both sides of the equation, it comes down to the type:**

*ψ (x)*If we can solve the equation obtained in this way, the obtained solutions are also solutions of the given equation.

* 4) Solving the equation of the form *When a

**nd a**

*> 0 a***a**

*≠ 1,**) is an algebraic function, by changing a ^ f*

**nd f (x***e equation is reduced to the type:*

**(x) th***F (t) = 0*

If the last equation has solutions** t₁ t₂, t₃, … tk**, then the equation under consideration comes down to solving the set of exponential equations: