To determine unique constants $x,y$, interpret the equality as an identity for all independent pos

Question

To determine unique constants $x,y$, interpret the equality as an identity for all independent positive bases $m,n$. For fixed unspecified $m,n$, one equation generally does not determine both unknowns. If $\frac{m^x}{n^y} \times \frac{n^{4-3x}}{(m^{y+1})^2} = \frac{n^7}{m^{10}}$, find the value(s) of $x$ and $y$.

Accepted Answer

Under the identity interpretation, $x=-2$, $y=3$. Otherwise the given information is generally insufficient.

Exponential and Logarithmic Functions - Simultaneous Exponential Equations

Exponential and Logarithmic Functions - Simultaneous Exponential Equations

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