Question

please solve the question
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Answer 1

Question

$\sf \: If \: 9^{x+2} = 720 + 9^{x} \: \\ \sf \: Find \: the \: value \: of 4x^{\frac{1}{x}}$

Solution

$9^{x+2} = 720 + 9^{x} \\ 9^{x+2} - 9^{x} = 720 \\ {9}^{x} ( {9}^{2} - 1) = 720 \\ {9}^{x} ( 81 - 1) = 720 \\ {9}^{x} ( 80) = 720 \\ {9}^{x} = \frac{720}{80} = 9 \\ {9}^{x} = {9}^{1} \\ \boxed{\boxed{x = 1}}$

Now,

$= 4x ^{ \frac{1}{x} } \\ = 4 \times {1}^{ \frac{1}{1} } \\ = 4 \times 1 \\ = 4$

Final answer

Therefore, The required answer is 4