Exponential equations

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 and a ≠ 1 is equivalent to the equation f (x) = ψ (x).



3) Solve the equation of sight


a> 0, a ≠ 1; b> 0, b 1, a f (x) and ψ (x) are given algebraic functions, by logarithmizing both sides of the equation, it comes down to the type:


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> 0 and a ≠ 1, and f (x) is an algebraic function, by changing a ^ f (x) the equation is reduced to the type:

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:


– exponential equations –

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