Question 91693
{{{ln(x) = 3ln(y)}}}
{{{ln(x) = ln(y^3)}}}
{{{ln(x) - ln(y^3) = 0}}}
{{{ln(x/y^3) = 0}}}
{{{x/y^3 = 1}}}
{{{x = y^3}}} __________ (1)


{{{3^x = 27^y}}}
{{{3^x = (3^3)^y}}}
{{{3^x = 3^(3y)}}}
{{{x = 3y}}} ___________ (2)


Substituting x from (1) in (2)
{{{y^3 = 3y}}}
{{{y^3 - 3y = 0}}}
{{{y(y^2 - 3) = 0}}}
{{{y(y + sqrt(3))(y - sqrt(3)) = 0}}}
Either {{{y = 0}}}, {{{y = - sqrt(3)}}} or {{{y = sqrt(3)}}}
Accordingly, {{{x = 0}}}, {{{x = - 3sqrt(3)}}} or {{{x = 3sqrt(3)}}}


But since logarithm of negative numbers is undefined so {{{x = -3sqrt(3)}}},{{{y = -sqrt(3)}}} is not a solution.


Hence, the solutions are {{{x = 0}}},{{{ y = 0}}}and {{{x = 3sqrt(3)}}},{{{y = sqrt(3)}}}.