The number of solutions of the equation $32^{\tan^{2} x} + 32^{\sec^{2} x} = 81, 0 \leq x \leq \frac{π}{4}$ is ___________

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Detailed Solution

$32^{\tan^{2} x} + 32^{1 + \tan^{2} x} = 81 \Rightarrow 32^{\tan^{2} x} (1 + 32) = 81$
$32^{\tan^{2} x} = \frac{81}{33} \Rightarrow \tan^{2} x = \log_{32} \frac{81}{33}$ Only one solution in $[0, \frac{π}{4}]$

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