How to solve $log_frac13(frac3x-1x+2)>0$. [closed]

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How to solve




$$log_frac13(dfrac3x-1x+2)>0$$




I am not sure how to solve it.




algebra-precalculus inequality




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closed as off-topic by amWhy, Claude Leibovici, Taroccoesbrocco, Xander Henderson, user223391 Jul 30 at 0:04


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Claude Leibovici, Taroccoesbrocco, Xander Henderson, Community
If this question can be reworded to fit the rules in the help center, please edit the question.












  • Hint $log(fracab) = log(a) - log(b)$
    – Good Morning Captain
    Jul 28 at 16:56











  • @GoodMorningCaptain this only if numerator and denominator are both positive.
    – Vera
    Jul 28 at 16:57














up vote
0
down vote

favorite












How to solve




$$log_frac13(dfrac3x-1x+2)>0$$




I am not sure how to solve it.




algebra-precalculus inequality




share|cite|improve this question













closed as off-topic by amWhy, Claude Leibovici, Taroccoesbrocco, Xander Henderson, user223391 Jul 30 at 0:04


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Claude Leibovici, Taroccoesbrocco, Xander Henderson, Community
If this question can be reworded to fit the rules in the help center, please edit the question.












  • Hint $log(fracab) = log(a) - log(b)$
    – Good Morning Captain
    Jul 28 at 16:56











  • @GoodMorningCaptain this only if numerator and denominator are both positive.
    – Vera
    Jul 28 at 16:57












up vote
0
down vote

favorite









up vote
0
down vote

favorite











How to solve




$$log_frac13(dfrac3x-1x+2)>0$$




I am not sure how to solve it.




algebra-precalculus inequality




share|cite|improve this question













How to solve




$$log_frac13(dfrac3x-1x+2)>0$$




I am not sure how to solve it.





algebra-precalculus inequality





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited Jul 28 at 17:06









user 108128

19k41544




19k41544









asked Jul 28 at 16:54









UltimateMath

385




385




closed as off-topic by amWhy, Claude Leibovici, Taroccoesbrocco, Xander Henderson, user223391 Jul 30 at 0:04


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Claude Leibovici, Taroccoesbrocco, Xander Henderson, Community
If this question can be reworded to fit the rules in the help center, please edit the question.




closed as off-topic by amWhy, Claude Leibovici, Taroccoesbrocco, Xander Henderson, user223391 Jul 30 at 0:04


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – amWhy, Claude Leibovici, Taroccoesbrocco, Xander Henderson, Community
If this question can be reworded to fit the rules in the help center, please edit the question.











  • Hint $log(fracab) = log(a) - log(b)$
    – Good Morning Captain
    Jul 28 at 16:56











  • @GoodMorningCaptain this only if numerator and denominator are both positive.
    – Vera
    Jul 28 at 16:57
















  • Hint $log(fracab) = log(a) - log(b)$
    – Good Morning Captain
    Jul 28 at 16:56











  • @GoodMorningCaptain this only if numerator and denominator are both positive.
    – Vera
    Jul 28 at 16:57















Hint $log(fracab) = log(a) - log(b)$
– Good Morning Captain
Jul 28 at 16:56





Hint $log(fracab) = log(a) - log(b)$
– Good Morning Captain
Jul 28 at 16:56













@GoodMorningCaptain this only if numerator and denominator are both positive.
– Vera
Jul 28 at 16:57




@GoodMorningCaptain this only if numerator and denominator are both positive.
– Vera
Jul 28 at 16:57










2 Answers
2






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up vote
2
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accepted










Hint:
$$log_(1/3)left(frac3x-1x+2right)=-log_3left(frac3x-1x+2right)=log_3left(fracx+23x-1right)>0.$$
Note that $log_a t>0$ if and only if $t>1$ (when $a>1$).






share|cite|improve this answer






























    up vote
    0
    down vote













    Note:
    $$log_frac13(k)>0 text when 0<k<1$$



    So you want when:
    $$0<frac3x-1x+2<1$$
    $$to0^2<frac(3x-1)^2(x+2)^2<1^2$$
    $$to0^2(x+2)^2<(3x-1)^2<1^2(x+2)^2$$
    $$to0<(3x-1)^2<(x+2)^2$$
    Now continue this by finding all $x$ which satisfy:
    $$(x+2)^2>(3x-1)^2text AND (3x-1)^2>0$$






    share|cite|improve this answer




























      2 Answers
      2






      active

      oldest

      votes








      2 Answers
      2






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes








      up vote
      2
      down vote



      accepted










      Hint:
      $$log_(1/3)left(frac3x-1x+2right)=-log_3left(frac3x-1x+2right)=log_3left(fracx+23x-1right)>0.$$
      Note that $log_a t>0$ if and only if $t>1$ (when $a>1$).






      share|cite|improve this answer



























        up vote
        2
        down vote



        accepted










        Hint:
        $$log_(1/3)left(frac3x-1x+2right)=-log_3left(frac3x-1x+2right)=log_3left(fracx+23x-1right)>0.$$
        Note that $log_a t>0$ if and only if $t>1$ (when $a>1$).






        share|cite|improve this answer

























          up vote
          2
          down vote



          accepted







          up vote
          2
          down vote



          accepted






          Hint:
          $$log_(1/3)left(frac3x-1x+2right)=-log_3left(frac3x-1x+2right)=log_3left(fracx+23x-1right)>0.$$
          Note that $log_a t>0$ if and only if $t>1$ (when $a>1$).






          share|cite|improve this answer















          Hint:
          $$log_(1/3)left(frac3x-1x+2right)=-log_3left(frac3x-1x+2right)=log_3left(fracx+23x-1right)>0.$$
          Note that $log_a t>0$ if and only if $t>1$ (when $a>1$).







          share|cite|improve this answer















          share|cite|improve this answer



          share|cite|improve this answer








          edited Aug 3 at 11:23









          amWhy

          189k25219431




          189k25219431











          answered Jul 28 at 16:58









          user 108128

          19k41544




          19k41544




















              up vote
              0
              down vote













              Note:
              $$log_frac13(k)>0 text when 0<k<1$$



              So you want when:
              $$0<frac3x-1x+2<1$$
              $$to0^2<frac(3x-1)^2(x+2)^2<1^2$$
              $$to0^2(x+2)^2<(3x-1)^2<1^2(x+2)^2$$
              $$to0<(3x-1)^2<(x+2)^2$$
              Now continue this by finding all $x$ which satisfy:
              $$(x+2)^2>(3x-1)^2text AND (3x-1)^2>0$$






              share|cite|improve this answer

























                up vote
                0
                down vote













                Note:
                $$log_frac13(k)>0 text when 0<k<1$$



                So you want when:
                $$0<frac3x-1x+2<1$$
                $$to0^2<frac(3x-1)^2(x+2)^2<1^2$$
                $$to0^2(x+2)^2<(3x-1)^2<1^2(x+2)^2$$
                $$to0<(3x-1)^2<(x+2)^2$$
                Now continue this by finding all $x$ which satisfy:
                $$(x+2)^2>(3x-1)^2text AND (3x-1)^2>0$$






                share|cite|improve this answer























                  up vote
                  0
                  down vote










                  up vote
                  0
                  down vote









                  Note:
                  $$log_frac13(k)>0 text when 0<k<1$$



                  So you want when:
                  $$0<frac3x-1x+2<1$$
                  $$to0^2<frac(3x-1)^2(x+2)^2<1^2$$
                  $$to0^2(x+2)^2<(3x-1)^2<1^2(x+2)^2$$
                  $$to0<(3x-1)^2<(x+2)^2$$
                  Now continue this by finding all $x$ which satisfy:
                  $$(x+2)^2>(3x-1)^2text AND (3x-1)^2>0$$






                  share|cite|improve this answer













                  Note:
                  $$log_frac13(k)>0 text when 0<k<1$$



                  So you want when:
                  $$0<frac3x-1x+2<1$$
                  $$to0^2<frac(3x-1)^2(x+2)^2<1^2$$
                  $$to0^2(x+2)^2<(3x-1)^2<1^2(x+2)^2$$
                  $$to0<(3x-1)^2<(x+2)^2$$
                  Now continue this by finding all $x$ which satisfy:
                  $$(x+2)^2>(3x-1)^2text AND (3x-1)^2>0$$







                  share|cite|improve this answer













                  share|cite|improve this answer



                  share|cite|improve this answer











                  answered Jul 28 at 17:17









                  Rhys Hughes

                  3,8581227




                  3,8581227












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