Question

9 raise to power x + 2 is equal to 720 + 9 raise to power x

Answer 1

Hi,

Here is your answer !
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${9}^{x + 2} = 720 + {9}^{x} \\ \\ \implies {9}^{x + 2} - {9}^{x} = 720 \\ \\\implies {9}^{x} . {9}^{2} - {9}^{x} = 720 \\ \: \:\: \: \: \: \: \:\: \:\: \: \: \:\: \:\: \:\: \: \: \: \: \:\: \:\: \:\: \:[ \because {a}^{m + n} = {a}^{m} \times {a}^{n} ]\\ \\\implies {9}^{x} \times ( {9}^{2} - 1) = 720 \\ \\ \implies {9}^{x} \times (81 - 1) = 720 \\ \\\implies {9}^{x} \times 80 = 720 \\ \\ \implies {9}^{x} = \frac{720}{80} \\ \\\implies {9}^{x} = {9}^{1}$
On equating the power of 9, We get

$x = 1$