Question 1178302
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Note that the two equations involve {{{log(x,y)}}} and {{{log(y,x)}}}.  Somewhere in working the problem you are going to want to use this property of logarithms:<br>
{{{log(y,x) = 1/log(x,y)}}}<br>
Work with the first equation:<br>
{{{log(x,y^4)=m^3}}}
{{{4*log(x,y)=m^3}}}
{{{log(x,y)=m^3/4}}}
{{{log(y,x)=1/((m^3/4))=4/m^3}}}<br>
Now look at the second equation:<br>
{{{log(y,x)=4/m^2}}}<br>
The two expressions for {{{log(y,x)}}} must be equal:<br>
{{{4/m^3=4/m^2}}}
{{{4m^3=4m^2}}}
{{{m=1}}}<br>