Mathematica can't simplify some logarithmic expressions

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When I simplify some logarithmic expressions in Mathematica, it just returns the expression



FullSimplify[Log[Sqrt[2] + 1, 5 Sqrt[2] + 7]]

FullSimplify[Log[Sqrt[2] + 1, 17 - 12 Sqrt[2]]]


enter image description here



Obviously, simplification isn't completely, using Maple could get
enter image description here



Is there any way I can tell Mathematica to be smarter?






simplifying-expressions algebraic-manipulation







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    up vote
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    down vote

    favorite
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    When I simplify some logarithmic expressions in Mathematica, it just returns the expression



    FullSimplify[Log[Sqrt[2] + 1, 5 Sqrt[2] + 7]]

    FullSimplify[Log[Sqrt[2] + 1, 17 - 12 Sqrt[2]]]


    enter image description here



    Obviously, simplification isn't completely, using Maple could get
    enter image description here



    Is there any way I can tell Mathematica to be smarter?






    simplifying-expressions algebraic-manipulation







    share|improve this question

























      up vote
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      down vote

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      up vote
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      When I simplify some logarithmic expressions in Mathematica, it just returns the expression



      FullSimplify[Log[Sqrt[2] + 1, 5 Sqrt[2] + 7]]

      FullSimplify[Log[Sqrt[2] + 1, 17 - 12 Sqrt[2]]]


      enter image description here



      Obviously, simplification isn't completely, using Maple could get
      enter image description here



      Is there any way I can tell Mathematica to be smarter?






      simplifying-expressions algebraic-manipulation







      share|improve this question















      When I simplify some logarithmic expressions in Mathematica, it just returns the expression



      FullSimplify[Log[Sqrt[2] + 1, 5 Sqrt[2] + 7]]

      FullSimplify[Log[Sqrt[2] + 1, 17 - 12 Sqrt[2]]]


      enter image description here



      Obviously, simplification isn't completely, using Maple could get
      enter image description here



      Is there any way I can tell Mathematica to be smarter?






      simplifying-expressions algebraic-manipulation




      simplifying-expressions algebraic-manipulation






      share|improve this question















      share|improve this question













      share|improve this question




      share|improve this question








      edited 1 hour ago

























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      mathe

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          Use RootApproximant



          y1 = Log[Sqrt[2] + 1, 5 Sqrt[2] + 7];

          y1 // RootApproximant

          (* 3 *)


          Verifying,



          y1 == 3 // FullSimplify

          (* True *)

          y2 = Log[2 Sqrt[2] + 3, 17 - 12 Sqrt[2]];

          y2 // RootApproximant

          (* -2 *)


          Verifying,



          y2 == -2 // FullSimplify

          (* True *)





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            Use RootApproximant



            y1 = Log[Sqrt[2] + 1, 5 Sqrt[2] + 7];

            y1 // RootApproximant

            (* 3 *)


            Verifying,



            y1 == 3 // FullSimplify

            (* True *)

            y2 = Log[2 Sqrt[2] + 3, 17 - 12 Sqrt[2]];

            y2 // RootApproximant

            (* -2 *)


            Verifying,



            y2 == -2 // FullSimplify

            (* True *)





            share|improve this answer
























              up vote
              4
              down vote













              Use RootApproximant



              y1 = Log[Sqrt[2] + 1, 5 Sqrt[2] + 7];

              y1 // RootApproximant

              (* 3 *)


              Verifying,



              y1 == 3 // FullSimplify

              (* True *)

              y2 = Log[2 Sqrt[2] + 3, 17 - 12 Sqrt[2]];

              y2 // RootApproximant

              (* -2 *)


              Verifying,



              y2 == -2 // FullSimplify

              (* True *)





              share|improve this answer






















                up vote
                4
                down vote










                up vote
                4
                down vote









                Use RootApproximant



                y1 = Log[Sqrt[2] + 1, 5 Sqrt[2] + 7];

                y1 // RootApproximant

                (* 3 *)


                Verifying,



                y1 == 3 // FullSimplify

                (* True *)

                y2 = Log[2 Sqrt[2] + 3, 17 - 12 Sqrt[2]];

                y2 // RootApproximant

                (* -2 *)


                Verifying,



                y2 == -2 // FullSimplify

                (* True *)





                share|improve this answer












                Use RootApproximant



                y1 = Log[Sqrt[2] + 1, 5 Sqrt[2] + 7];

                y1 // RootApproximant

                (* 3 *)


                Verifying,



                y1 == 3 // FullSimplify

                (* True *)

                y2 = Log[2 Sqrt[2] + 3, 17 - 12 Sqrt[2]];

                y2 // RootApproximant

                (* -2 *)


                Verifying,



                y2 == -2 // FullSimplify

                (* True *)






                share|improve this answer












                share|improve this answer



                share|improve this answer










                answered 1 hour ago









                Bob Hanlon

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