Explicație pas cu pas:
[tex] {x}^{2 + log_{3}(x) } = 27[/tex]
[tex]log_{3}({x}^{2 + log_{3}(x) }) = log_{3}( {3}^{3} )[/tex]
[tex](2 + log_{3}(x))log_{3}(x) = 3[/tex]
[tex]2log_{3}(x) + {{log} _{3}(x)}^{2} - 3 = 0 [/tex]
[tex]({log} _{3}(x) + 3)({log} _{3}(x) - 1) = 0[/tex]
[tex]{log} _{3}(x) + 3 = 0 \iff {log} _{3}(x) = - 3 \\ \implies \bf x = {3}^{ - 3} \iff x = \frac{1}{27} [/tex]
[tex]{log} _{3}(x) - 1 = 0 \iff {log} _{3}(x) = 1 \\ \implies \bf x = 3[/tex]
