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Notice that $\dfrac1{\log_ab} = \log_ba$ and $c^{\log_c a} = a$.

We will call the first equation (1) and the second equation (2).

$\quad 81^{1/\log_53} + 27^{\log_936}+3^{4/\log_79}\\ \stackrel{(1)}{=} 3^{4\log_35} + 9^{1.5\log_936} + 9^{2\log_97}\\ \stackrel{(2)}{=} 5^4 + 36^{1.5} + 7^2$

The rest is simple.