Question 244998
<pre>
given log(base a)x=4, log(base a)y=3, and log(base a)z=2 for constants x, y,z. find the value of the logarithm.

log(base a)((5th root of y^3 times x^6 times z^4)/(5th root of z^6 times x^2)

         {{{log(a, ((root (5, y^3x^6z^4))/(root (5, z^6x^2))))}}}

         {{{log(a, (root (5, (y^3x^6z^4)/x^2z^6)))}}} ---- Applying {{{root (b,  c)/root (b, d)}}} = {{{root (b, c/d)}}}
          {{{log(a, ((y^3x^6z^4)/(x^2z^6))^(1/5))}}} --- Applying {{{root (b, c)}}} = {{{matrix(2,1, " ", c^(1/b))}}}
        {{{log(a, ((y^3x^4cross(x^6)cross(z^4))/(cross(x^2)z^2cross(z^6)))^(1/5))}}}
           {{{log(a, ((y^3x^4)/z^2)^(1/5))}}}
           {{{(1/5)log(a, ((y^3x^4)/z^2))}}} ---- Applying {{{log (b, (c^d))}}} = {{{d*log (b,  (c))}}}
           {{{(1/5)(log(a, (y^3)) + log (a, (x^4)) - log (a, (z^2)))}}}   
           {{{(1/5)(3log(a, (y)) + 4log (a, (x)) - 2log (a, (z)))}}} ----- Applying {{{log (b, (c^d))}}} = {{{d*log (b, (c))}}}
           {{{(1/5)(3(3) + 4(4) - 2(2))}}} ---- Substituting {{{system(matrix(3,3, 3, for, log (a, (y)), 4, for, log (a, (x)), 2, for, log (a, (z)))))}}}
          {{{(1/5)(9 + 16 - 4)}}}
          {{{highlight_green((1/5)(21) = highlight(21/5))}}}</pre>