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| 1 | The article is devoted to the solutions to the equations containing the unknown at the base and index. A detailed analysis of the problem proved that there is no decisive answer as to what conditions need to be imposed on the equation function. The primary way of solving such equations is taking the logarithm of both members of the equation, in this case some roots are lost. It should be noted that equations of such type are studied at school and pupils are to master the skills of solution to such equations. The article suggests algorythm of solution of these equations, analyses certain examples. The conclusions are drawn that solving such equations can greatly contribute to the development of students’ logical thinking as well as their abilities, intuition and cognitive power. Keywords: power function, equation root, acceptable region, complex exponent | 1481 | ||||