Question

The value of $81^{(1 / \log_{5} 3)} + 27^{\log_{9} 36} + 3^{4 / \log_{7} 9}$ is equal to

Easy

Solution

$81^{(1 / \log_{5} 3)} + 27^{\log_{9} 36} + 3^{4 / \log_{7} 9}$
$= 3^{4 \log_{3} 5} + 3^{3 . \frac{1}{2} \log_{3} 36} + 3^{4 \log_{9} 7}$
$= 3^{\log_{3} 5^{4}} + 3^{\log_{3} 36^{3 / 2}} + 3^{\log_{3} 7^{4 / 2}}$
$= 5^{4} + 36^{3 / 2} + 7^{2} = 890 .$

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