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Compute  \( \large 81^{1/\log_5 3} + 27^{\log_9 36} + 3^{4 /\log_7 9}\)

 Jun 18, 2020
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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.

 Jun 18, 2020

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