If $9^{x + 2} = 720 + 9^{x}$ , find the value of $(4 x)^{1 / x}$ .

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Solution

$9^{x + 2} = 720 + 9^{x}$

$9^{x} \times 9^{2} = 720 + 9^{x}$

$9^{x} \times 9^{2} - 9^{x} = 720$

$9^{x} (9^{2} - 1) = 720$

$9^{x} \times 80 = 720$

$9^{x} = 9^{1}$

As the bases are same, equating the powers

$∴ x = 1$

Therefore,

$(4 x)^{1 / x} = (4 \times 1) = 4$

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