Solving for $x$ in $y=Ncdotleft(frac{10}{x}right)^{-2.6}$












1












$begingroup$


I want to confirm my solution of $x$ from
$$y=Ncdotleft(frac{10}{x}right)^{-2.6}$$
My answer is:
$$x=frac{N^{2.6}}{10cdot y^{2.6}}$$
Is this right? How would you solve?






algebra-precalculus







share|cite|improve this question











$endgroup$

















    1












    $begingroup$


    I want to confirm my solution of $x$ from
    $$y=Ncdotleft(frac{10}{x}right)^{-2.6}$$
    My answer is:
    $$x=frac{N^{2.6}}{10cdot y^{2.6}}$$
    Is this right? How would you solve?






    algebra-precalculus







    share|cite|improve this question











    $endgroup$















      1












      1








      1





      $begingroup$


      I want to confirm my solution of $x$ from
      $$y=Ncdotleft(frac{10}{x}right)^{-2.6}$$
      My answer is:
      $$x=frac{N^{2.6}}{10cdot y^{2.6}}$$
      Is this right? How would you solve?






      algebra-precalculus







      share|cite|improve this question











      $endgroup$




      I want to confirm my solution of $x$ from
      $$y=Ncdotleft(frac{10}{x}right)^{-2.6}$$
      My answer is:
      $$x=frac{N^{2.6}}{10cdot y^{2.6}}$$
      Is this right? How would you solve?






      algebra-precalculus




      algebra-precalculus






      share|cite|improve this question















      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited Jan 13 at 19:02







      user3063

















      asked Jan 13 at 8:12









      user3063user3063

      1143




      1143






















          2 Answers
          2






          active

          oldest

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          1












          $begingroup$

          First, notice that
          $$
          y = N cdot left( dfrac{10}{x} right)^{-2.6} = N cdot left( dfrac{x}{10} right)^{2.6}
          $$
          Next, divide both sides by $N$:
          $$
          dfrac{y}{N} = left( dfrac{x}{10} right)^{2.6}
          $$
          Now exponentiate with $frac{1}{2.6}$ to get
          $$
          left( dfrac{y}{N} right)^{frac{1}{2.6}} = dfrac{x}{10}
          $$
          Finally, multiply by $10$:
          $$
          10 cdot left( dfrac{y}{N} right)^{frac{1}{2.6}} = x
          $$






          share|cite|improve this answer









          $endgroup$









          • 1




            $begingroup$
            Thank you so much!
            $endgroup$
            – user3063
            Jan 13 at 10:07



















          1












          $begingroup$

          Let $$y = N cdot (frac{10}{x})^{-2.6}$$



          Then,



          $$y cdot (frac{10}{x})^{2.6} = N$$



          $$ y cdot 10 ^{2.6} = N cdot x^{2.6}$$



          $$ (y cdot 10^{2.6})^{1/2.6} = (N cdot x^{2.6})^{1/2.6}$$



          $$ y^{1/2.6} cdot 10 = N^{1/2.6} cdot x$$



          $$ x = y^{1/2.6} cdot 10 cdot N^{-1/2.6} = (frac{y}{N})^{1/2.6} cdot 10 $$






          share|cite|improve this answer











          $endgroup$













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            2 Answers
            2






            active

            oldest

            votes








            2 Answers
            2






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes









            1












            $begingroup$

            First, notice that
            $$
            y = N cdot left( dfrac{10}{x} right)^{-2.6} = N cdot left( dfrac{x}{10} right)^{2.6}
            $$
            Next, divide both sides by $N$:
            $$
            dfrac{y}{N} = left( dfrac{x}{10} right)^{2.6}
            $$
            Now exponentiate with $frac{1}{2.6}$ to get
            $$
            left( dfrac{y}{N} right)^{frac{1}{2.6}} = dfrac{x}{10}
            $$
            Finally, multiply by $10$:
            $$
            10 cdot left( dfrac{y}{N} right)^{frac{1}{2.6}} = x
            $$






            share|cite|improve this answer









            $endgroup$









            • 1




              $begingroup$
              Thank you so much!
              $endgroup$
              – user3063
              Jan 13 at 10:07
















            1












            $begingroup$

            First, notice that
            $$
            y = N cdot left( dfrac{10}{x} right)^{-2.6} = N cdot left( dfrac{x}{10} right)^{2.6}
            $$
            Next, divide both sides by $N$:
            $$
            dfrac{y}{N} = left( dfrac{x}{10} right)^{2.6}
            $$
            Now exponentiate with $frac{1}{2.6}$ to get
            $$
            left( dfrac{y}{N} right)^{frac{1}{2.6}} = dfrac{x}{10}
            $$
            Finally, multiply by $10$:
            $$
            10 cdot left( dfrac{y}{N} right)^{frac{1}{2.6}} = x
            $$






            share|cite|improve this answer









            $endgroup$









            • 1




              $begingroup$
              Thank you so much!
              $endgroup$
              – user3063
              Jan 13 at 10:07














            1












            1








            1





            $begingroup$

            First, notice that
            $$
            y = N cdot left( dfrac{10}{x} right)^{-2.6} = N cdot left( dfrac{x}{10} right)^{2.6}
            $$
            Next, divide both sides by $N$:
            $$
            dfrac{y}{N} = left( dfrac{x}{10} right)^{2.6}
            $$
            Now exponentiate with $frac{1}{2.6}$ to get
            $$
            left( dfrac{y}{N} right)^{frac{1}{2.6}} = dfrac{x}{10}
            $$
            Finally, multiply by $10$:
            $$
            10 cdot left( dfrac{y}{N} right)^{frac{1}{2.6}} = x
            $$






            share|cite|improve this answer









            $endgroup$



            First, notice that
            $$
            y = N cdot left( dfrac{10}{x} right)^{-2.6} = N cdot left( dfrac{x}{10} right)^{2.6}
            $$
            Next, divide both sides by $N$:
            $$
            dfrac{y}{N} = left( dfrac{x}{10} right)^{2.6}
            $$
            Now exponentiate with $frac{1}{2.6}$ to get
            $$
            left( dfrac{y}{N} right)^{frac{1}{2.6}} = dfrac{x}{10}
            $$
            Finally, multiply by $10$:
            $$
            10 cdot left( dfrac{y}{N} right)^{frac{1}{2.6}} = x
            $$







            share|cite|improve this answer












            share|cite|improve this answer



            share|cite|improve this answer










            answered Jan 13 at 9:22









            Björn FriedrichBjörn Friedrich

            2,67461831




            2,67461831








            • 1




              $begingroup$
              Thank you so much!
              $endgroup$
              – user3063
              Jan 13 at 10:07














            • 1




              $begingroup$
              Thank you so much!
              $endgroup$
              – user3063
              Jan 13 at 10:07








            1




            1




            $begingroup$
            Thank you so much!
            $endgroup$
            – user3063
            Jan 13 at 10:07




            $begingroup$
            Thank you so much!
            $endgroup$
            – user3063
            Jan 13 at 10:07











            1












            $begingroup$

            Let $$y = N cdot (frac{10}{x})^{-2.6}$$



            Then,



            $$y cdot (frac{10}{x})^{2.6} = N$$



            $$ y cdot 10 ^{2.6} = N cdot x^{2.6}$$



            $$ (y cdot 10^{2.6})^{1/2.6} = (N cdot x^{2.6})^{1/2.6}$$



            $$ y^{1/2.6} cdot 10 = N^{1/2.6} cdot x$$



            $$ x = y^{1/2.6} cdot 10 cdot N^{-1/2.6} = (frac{y}{N})^{1/2.6} cdot 10 $$






            share|cite|improve this answer











            $endgroup$


















              1












              $begingroup$

              Let $$y = N cdot (frac{10}{x})^{-2.6}$$



              Then,



              $$y cdot (frac{10}{x})^{2.6} = N$$



              $$ y cdot 10 ^{2.6} = N cdot x^{2.6}$$



              $$ (y cdot 10^{2.6})^{1/2.6} = (N cdot x^{2.6})^{1/2.6}$$



              $$ y^{1/2.6} cdot 10 = N^{1/2.6} cdot x$$



              $$ x = y^{1/2.6} cdot 10 cdot N^{-1/2.6} = (frac{y}{N})^{1/2.6} cdot 10 $$






              share|cite|improve this answer











              $endgroup$
















                1












                1








                1





                $begingroup$

                Let $$y = N cdot (frac{10}{x})^{-2.6}$$



                Then,



                $$y cdot (frac{10}{x})^{2.6} = N$$



                $$ y cdot 10 ^{2.6} = N cdot x^{2.6}$$



                $$ (y cdot 10^{2.6})^{1/2.6} = (N cdot x^{2.6})^{1/2.6}$$



                $$ y^{1/2.6} cdot 10 = N^{1/2.6} cdot x$$



                $$ x = y^{1/2.6} cdot 10 cdot N^{-1/2.6} = (frac{y}{N})^{1/2.6} cdot 10 $$






                share|cite|improve this answer











                $endgroup$



                Let $$y = N cdot (frac{10}{x})^{-2.6}$$



                Then,



                $$y cdot (frac{10}{x})^{2.6} = N$$



                $$ y cdot 10 ^{2.6} = N cdot x^{2.6}$$



                $$ (y cdot 10^{2.6})^{1/2.6} = (N cdot x^{2.6})^{1/2.6}$$



                $$ y^{1/2.6} cdot 10 = N^{1/2.6} cdot x$$



                $$ x = y^{1/2.6} cdot 10 cdot N^{-1/2.6} = (frac{y}{N})^{1/2.6} cdot 10 $$







                share|cite|improve this answer














                share|cite|improve this answer



                share|cite|improve this answer








                edited Jan 13 at 9:05

























                answered Jan 13 at 8:51









                idriskameniidriskameni

                734321




                734321






























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