Question 1046159
{{{logx/a=logy/2=logz/5}}} <===> {{{log(x^(1/a))=log(y^(1/2))=log(z^(1/5))}}}  <===>  {{{x^(1/a)=y^(1/2)=z^(1/5)}}} 

===> {{{x^2 = y^a}}},   {{{y^5 = z^2}}}, and  {{{x^5 = z^a}}}.

The first equation implies that {{{x^4 = y^(2a)}}}.

From the given, {{{x^4*y^3*z^(-2)=1}}}, or  {{{x^4*y^3 = z^2}}},

===> {{{y^(2a)*y^3 = y^5}}}, after direct substitution.

===> {{{y^(2a+3) = y^5}}}, or, {{{highlight(a = 1)}}}.

N.B.: The value of k in the statement of the problem is irrelevant in getting the value of a.