If $frac {a}{3^{x-1}}=frac{b}{3^{y+2}}=frac{c}{3^{z-1}}=frac 15;$ then which of the following equals...

Multi tool use
Multi tool use












2












$begingroup$


The problem is:




If $frac {a}{3^{x-1}}=frac{b}{3^{y+2}}=frac{c}{3^{z-1}}=frac 15,;$ then which of the following equals $a×b×c$ ?



A) $frac {1}{375}$



B) $frac{1}{125}$



C) $frac{27}{125}$



D) $frac{3}{125}$



E) $frac{27}{5}$




I think the question is wrong.



My counterexample:




Let $x=m,; y=m-3,; z=m.$



Then $a=b=c=frac{3^{m-1}}{5}.$



So, $a×b×c=frac{3^{3m-3}}{125},; minmathbb{R}.$




Am I right?






algebra-precalculus proof-verification contest-math examples-counterexamples exponentiation







share|cite|improve this question











$endgroup$












  • $begingroup$
    "$a times b times c$ which of the following" maybe you need a verb for this sentence? :P
    $endgroup$
    – L. F.
    Dec 14 '18 at 8:28










  • $begingroup$
    @L.F. Or maybe only an "is" ;P
    $endgroup$
    – AryanSonwatikar
    Dec 14 '18 at 11:54








  • 3




    $begingroup$
    @ary Technically "is" is also a verb XD
    $endgroup$
    – L. F.
    Dec 14 '18 at 11:55
















2












$begingroup$


The problem is:




If $frac {a}{3^{x-1}}=frac{b}{3^{y+2}}=frac{c}{3^{z-1}}=frac 15,;$ then which of the following equals $a×b×c$ ?



A) $frac {1}{375}$



B) $frac{1}{125}$



C) $frac{27}{125}$



D) $frac{3}{125}$



E) $frac{27}{5}$




I think the question is wrong.



My counterexample:




Let $x=m,; y=m-3,; z=m.$



Then $a=b=c=frac{3^{m-1}}{5}.$



So, $a×b×c=frac{3^{3m-3}}{125},; minmathbb{R}.$




Am I right?






algebra-precalculus proof-verification contest-math examples-counterexamples exponentiation







share|cite|improve this question











$endgroup$












  • $begingroup$
    "$a times b times c$ which of the following" maybe you need a verb for this sentence? :P
    $endgroup$
    – L. F.
    Dec 14 '18 at 8:28










  • $begingroup$
    @L.F. Or maybe only an "is" ;P
    $endgroup$
    – AryanSonwatikar
    Dec 14 '18 at 11:54








  • 3




    $begingroup$
    @ary Technically "is" is also a verb XD
    $endgroup$
    – L. F.
    Dec 14 '18 at 11:55














2












2








2





$begingroup$


The problem is:




If $frac {a}{3^{x-1}}=frac{b}{3^{y+2}}=frac{c}{3^{z-1}}=frac 15,;$ then which of the following equals $a×b×c$ ?



A) $frac {1}{375}$



B) $frac{1}{125}$



C) $frac{27}{125}$



D) $frac{3}{125}$



E) $frac{27}{5}$




I think the question is wrong.



My counterexample:




Let $x=m,; y=m-3,; z=m.$



Then $a=b=c=frac{3^{m-1}}{5}.$



So, $a×b×c=frac{3^{3m-3}}{125},; minmathbb{R}.$




Am I right?






algebra-precalculus proof-verification contest-math examples-counterexamples exponentiation







share|cite|improve this question











$endgroup$




The problem is:




If $frac {a}{3^{x-1}}=frac{b}{3^{y+2}}=frac{c}{3^{z-1}}=frac 15,;$ then which of the following equals $a×b×c$ ?



A) $frac {1}{375}$



B) $frac{1}{125}$



C) $frac{27}{125}$



D) $frac{3}{125}$



E) $frac{27}{5}$




I think the question is wrong.



My counterexample:




Let $x=m,; y=m-3,; z=m.$



Then $a=b=c=frac{3^{m-1}}{5}.$



So, $a×b×c=frac{3^{3m-3}}{125},; minmathbb{R}.$




Am I right?






algebra-precalculus proof-verification contest-math examples-counterexamples exponentiation




algebra-precalculus proof-verification contest-math examples-counterexamples exponentiation






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Dec 14 '18 at 16:10









user376343

3,9234829




3,9234829










asked Dec 14 '18 at 8:04









ElementaryElementary

361111




361111












  • $begingroup$
    "$a times b times c$ which of the following" maybe you need a verb for this sentence? :P
    $endgroup$
    – L. F.
    Dec 14 '18 at 8:28










  • $begingroup$
    @L.F. Or maybe only an "is" ;P
    $endgroup$
    – AryanSonwatikar
    Dec 14 '18 at 11:54








  • 3




    $begingroup$
    @ary Technically "is" is also a verb XD
    $endgroup$
    – L. F.
    Dec 14 '18 at 11:55


















  • $begingroup$
    "$a times b times c$ which of the following" maybe you need a verb for this sentence? :P
    $endgroup$
    – L. F.
    Dec 14 '18 at 8:28










  • $begingroup$
    @L.F. Or maybe only an "is" ;P
    $endgroup$
    – AryanSonwatikar
    Dec 14 '18 at 11:54








  • 3




    $begingroup$
    @ary Technically "is" is also a verb XD
    $endgroup$
    – L. F.
    Dec 14 '18 at 11:55
















$begingroup$
"$a times b times c$ which of the following" maybe you need a verb for this sentence? :P
$endgroup$
– L. F.
Dec 14 '18 at 8:28




$begingroup$
"$a times b times c$ which of the following" maybe you need a verb for this sentence? :P
$endgroup$
– L. F.
Dec 14 '18 at 8:28












$begingroup$
@L.F. Or maybe only an "is" ;P
$endgroup$
– AryanSonwatikar
Dec 14 '18 at 11:54






$begingroup$
@L.F. Or maybe only an "is" ;P
$endgroup$
– AryanSonwatikar
Dec 14 '18 at 11:54






3




3




$begingroup$
@ary Technically "is" is also a verb XD
$endgroup$
– L. F.
Dec 14 '18 at 11:55




$begingroup$
@ary Technically "is" is also a verb XD
$endgroup$
– L. F.
Dec 14 '18 at 11:55










1 Answer
1






active

oldest

votes


















2












$begingroup$

Yes some information is missing, indeed we have that



$$frac {a}{3^{x-1}}=frac{b}{3^{y+2}}=frac{c}{3^{z-1}}=frac 15$$



then



$$abc=frac{3^{(x+y+z)}}{125}$$



then we need a condition for $t=x+y+zin mathbb R$, since $3^{t}$ can assume any value $in(0,infty)$.






share|cite|improve this answer











$endgroup$













    Your Answer





    StackExchange.ifUsing("editor", function () {
    return StackExchange.using("mathjaxEditing", function () {
    StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
    StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
    });
    });
    }, "mathjax-editing");

    StackExchange.ready(function() {
    var channelOptions = {
    tags: "".split(" "),
    id: "69"
    };
    initTagRenderer("".split(" "), "".split(" "), channelOptions);

    StackExchange.using("externalEditor", function() {
    // Have to fire editor after snippets, if snippets enabled
    if (StackExchange.settings.snippets.snippetsEnabled) {
    StackExchange.using("snippets", function() {
    createEditor();
    });
    }
    else {
    createEditor();
    }
    });

    function createEditor() {
    StackExchange.prepareEditor({
    heartbeatType: 'answer',
    autoActivateHeartbeat: false,
    convertImagesToLinks: true,
    noModals: true,
    showLowRepImageUploadWarning: true,
    reputationToPostImages: 10,
    bindNavPrevention: true,
    postfix: "",
    imageUploader: {
    brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
    contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
    allowUrls: true
    },
    noCode: true, onDemand: true,
    discardSelector: ".discard-answer"
    ,immediatelyShowMarkdownHelp:true
    });


    }
    });














    draft saved

    draft discarded


















    StackExchange.ready(
    function () {
    StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3039091%2fif-frac-a3x-1-fracb3y2-fracc3z-1-frac-15-then-whic%23new-answer', 'question_page');
    }
    );

    Post as a guest















    Required, but never shown

























    1 Answer
    1






    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    2












    $begingroup$

    Yes some information is missing, indeed we have that



    $$frac {a}{3^{x-1}}=frac{b}{3^{y+2}}=frac{c}{3^{z-1}}=frac 15$$



    then



    $$abc=frac{3^{(x+y+z)}}{125}$$



    then we need a condition for $t=x+y+zin mathbb R$, since $3^{t}$ can assume any value $in(0,infty)$.






    share|cite|improve this answer











    $endgroup$


















      2












      $begingroup$

      Yes some information is missing, indeed we have that



      $$frac {a}{3^{x-1}}=frac{b}{3^{y+2}}=frac{c}{3^{z-1}}=frac 15$$



      then



      $$abc=frac{3^{(x+y+z)}}{125}$$



      then we need a condition for $t=x+y+zin mathbb R$, since $3^{t}$ can assume any value $in(0,infty)$.






      share|cite|improve this answer











      $endgroup$
















        2












        2








        2





        $begingroup$

        Yes some information is missing, indeed we have that



        $$frac {a}{3^{x-1}}=frac{b}{3^{y+2}}=frac{c}{3^{z-1}}=frac 15$$



        then



        $$abc=frac{3^{(x+y+z)}}{125}$$



        then we need a condition for $t=x+y+zin mathbb R$, since $3^{t}$ can assume any value $in(0,infty)$.






        share|cite|improve this answer











        $endgroup$



        Yes some information is missing, indeed we have that



        $$frac {a}{3^{x-1}}=frac{b}{3^{y+2}}=frac{c}{3^{z-1}}=frac 15$$



        then



        $$abc=frac{3^{(x+y+z)}}{125}$$



        then we need a condition for $t=x+y+zin mathbb R$, since $3^{t}$ can assume any value $in(0,infty)$.







        share|cite|improve this answer














        share|cite|improve this answer



        share|cite|improve this answer








        edited Dec 14 '18 at 8:24

























        answered Dec 14 '18 at 8:18









        gimusigimusi

        92.9k84494




        92.9k84494






























            draft saved

            draft discarded




















































            Thanks for contributing an answer to Mathematics Stack Exchange!


            • Please be sure to answer the question. Provide details and share your research!

            But avoid …



            • Asking for help, clarification, or responding to other answers.

            • Making statements based on opinion; back them up with references or personal experience.


            Use MathJax to format equations. MathJax reference.


            To learn more, see our tips on writing great answers.




            draft saved


            draft discarded














            StackExchange.ready(
            function () {
            StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3039091%2fif-frac-a3x-1-fracb3y2-fracc3z-1-frac-15-then-whic%23new-answer', 'question_page');
            }
            );

            Post as a guest















            Required, but never shown





















































            Required, but never shown














            Required, but never shown












            Required, but never shown







            Required, but never shown

































            Required, but never shown














            Required, but never shown












            Required, but never shown







            Required, but never shown







            wVP4OCzd7 4yM3gFNEl Iz5GL0BPk TUeCsjJ K0GsNbc4MmDwvEme,gKOjk,3o3O
            -
            rMv,7IES83,0v0AD716TdYh6W4P7,UZD3 yP3VvScXcP 81vBFTkK cViPSwEXYBxE,093kmtRa7vMn 5NTo8x9c,8n6,Qon,r,hPU

            Popular posts from this blog

            Plaza Victoria

            Image
            Plaza Victoria Plaza Victoria en 2017 Otros nombres Plaza de La Victoria Localización El Almendral, Valparaíso, Chile Vías adyacentes Chacabuco, Molina, Plaza Victoria y Edwards Creación 1841 Metro Bellavista Ubicación 33°02′46″S 71°37′11″O  /  -33.04624167, -71.61980833 Coordenadas: 33°02′46″S 71°37′11″O  /  -33.04624167, -71.61980833 [editar datos en Wikidata] La Plaza Victoria , también llamada Plaza de la Victoria , [ 1 ] ​ es una plaza ubicada en el sector El Almendral del plan de la ciudad de Valparaíso, Chile, de importancia patrimonial, que incluye valiosas estatuas y especies vegetales. [ 2 ] ​ La plaza se creó como tal en la primera mitad del siglo XIX, tomando previamente los nombres de Plaza Nueva y Plaza de Orrego . Si bien desde sus inicios tuvo relevancia histórica, no fue sino a partir de fines de los años 1860 cuando comenzó a cobrar mayor importancia y se convirtió en uno de los principales centros sociales de l...
            Read more

            Puebla de Zaragoza

            Image
            Para otros usos de este término, véase Puebla (desambiguación). Heroica Puebla de Zaragoza Localidad De arriba a abajo de izquierda a derecha: Estrella de Puebla, Volcán Popocatépetl, Catedral de Puebla, Monumento a Ignacio Zaragoza, Estadio Cuauhtémoc, Angelópolis y Vista panorámica de la ciudad. Escudo Otros nombres: El relicario de América/ La ciudad de los Ángeles/ La Angelópolis Lema: Muy noble y muy leal ciudad de Puebla de los Ángeles Heroica Puebla de Zaragoza Localización de Heroica Puebla de Zaragoza en México Heroica Puebla de Zaragoza Localización de Heroica Puebla de Zaragoza en Puebla Mapa interactivo Coordenadas 19°03′05″N 98°13′04″O  /  19.051388888889, -98.217777777778 Coordenadas: 19°03′05″N 98°13′04″O  /  19.051388888889, -98.217777777778 Idioma oficial Español Entidad Localidad  • País   México  • Estado Puebla  • Municipio Puebla Presidente municipal Claudia Rivera Vivanc...
            Read more

            Estelada

            Image
            Estelada blava (estelada azul), bandera independentista catalana original y clásica. Estelada vermella (estelada roja), otra bandera del independentismo catalán, con connotaciones más izquierdistas. La estelada («estrellada» en idioma español) es una bandera utilizada por ciudadanos de ideología independentista de Cataluña o por movimientos pancatalanistas de la Comunidad Valenciana y Baleares. Su creador fue Vicenç Albert Ballester, [ 1 ] ​ quien se inspiró en las banderas de Cuba y de Puerto Rico para su creación. [ 2 ] ​ Índice 1 Historia 2 Tipos 2.1 Diseños más frecuentes 2.2 Otros diseños históricos o propuestos 2.3 Esteladas basadas en los colores de clubes deportivos 3 Referencias 4 Bibliografía 5 Enlaces externos Historia Documento más antiguo en que aparece la estelada. Se trata de un documento en inglés titulado What says Catalonia con fecha del 11 de septiembre de 1918 en el que el Comité Pro Cataluña, funda...
            Read more