If 2 x = 3 y = 6 − z and x , y , z ≠ 0 then prove that: 1 x + 1 y + 1 z = 0I have tried starting with taking logartithms, but that gives just some more equations.Any specific way to solve these type of problems?

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If       2    x    =      3    y    =      6          −      z       and   x  ,  y  ,  z  ≠  0 then prove that:      1    x    +      1    y    +      1    z    =  0I have tried starting with taking logartithms, but that gives just some more equations.Any specific way to solve these type of problems?

rioolpijpgp · Accepted Answer

2    x    =      3    y    =      6          −      z        =  k  say, then   2  =      k            1      x        ,  3  =      k            1      y        ,  6  =      k                    −        1            z       now can you go on?then       k                    −        1            z        =  6  =  2  ×  3  =      k            1      x        ×      k            1      y        =      k                      1        x            +                  1        y

arridsd9 · Accepted Answer

2    x    =      3    y    =      6          −      z        =  kso  x  =      log    2    ⁡  k  y  =      log    3    ⁡  k  z  =  −      log    6    ⁡  kso      1    x    +      1    y    +      1    z    =      log    k    ⁡  2  +  l  o      g    k    3  −      log    k    ⁡  6  =      log    k    ⁡            2      ×      3        6    =  0

If 2 x </msup> = 3 y </msup> = 6 &#x2

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