Question

O valor de $log _{x} (x \sqrt{x} )$ é:

Answer 1

Aplicando propriedades operatórias de raízes, potencias e logaritmos

       $log(x)[x \sqrt{x} ] = n \\ \\ log(x)[x. x^{ \frac{1}{2} } ]=n \\ \\ log(x)[ x^{ \frac{3}{2} } ]=n \\ \\ x^{ \frac{3}{2} } =x^n \\ \\ n= \frac{3}{2}$

                                       $log(x)[x \sqrt{x} ]= \frac{3}{2}$