Question

Me ajudem

a)Log (5x-4)na base 3
b)log(3x-1) na basr (1/2)maior igual log (2x+3) na base (1/2)

C) log(3X+5) na base 2>3

Answer 1

   a)
            log(3)[5x - 4] ???? INCOMPLETA
   b)
            $log( \frac{1}{2})[3x-1] \geq log( \frac{1}{2})[2x+3]$

                                                           Condição de existência: x > 1/3
                                                                  base ok
                                         $3x+5\ \textgreater \ 2^3 \\ \\ 3x\ \textgreater \ 8-5 \\ \\ 3x\ \textgreater \ 3$                         3x - 1 > 0
                                                                         3x > 1
                                                                                              x.I > 1/3
                                                                   2x + 3 > 0
                                                                          2x > - 3
                                                                                              x.II > - 3/2
                                                                                               (x.I)inter(x.II) = x.I
            3x - 1 > 2x + 3
          3x - 2x > 3 + 1
                 x > 4 CONCIÇÃO DE EXISTENCIA OK

                              x > 4 RESULTADO FINAL   
   c)
            log(2)[3x + 5] > 3
                                                 Condição de existência: x > - 5/3
                                                      base: ok
                                                     3x + 5 > 0
                                                           3x > - 5        
                                                             x > - 5/3  

 $3x+5\ \textgreater \ 2^3 \\ \\ 3x\ \textgreater \ 8-5 \\ \\ 3x\ \textgreater \ 3$

                                                   x > 1 CONDIÇÃO DE EXISTENCIA OK

                                                                          x > 1 RESULTADO FINAL