![Domain:\ x0\ \wedge\ x\neq1\ \wedge\ y0 \wedge\ y\neq1\\\\\underline{+\left\{\begin{array}{ccc}\log_x32+\log_y9=7\\\log_x32-\log_y9=3\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad2\log_x32=10\qquad\text{divide both sides by 2}\\.\qquad\log_x32=5\qquad\text{use}\ \log_ab=c\iff a^c=b\\.\qquad x^5=32\to x=\sqrt[5]{32}\to\boxed{x=2}\\\\\text{Substitute}\ \log_x32=5\ \text{to the first equation:}\\5+\log_y9=7\qquad\text{subtract 5 from both sides}](/tpl/images/0454/3935/42379.png)
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