Question

$3 {}^{2x } - 10 \times 3 {}^{x + 2} + 729 = 0$
PLZ ANS THE QUESTION



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Answer 1

Answer:

$x = 4 \: \: or \: x \: \: = \: 2$

Step-by-step explanation:

Given equation :

${3}^{2x} - 10 \: \times {3}^{x \: + 2} + 729 = 0$

${3}^{2x} - 10 \times {3}^{2} \times {3}^{x} + 729 = 0$

${ ({3}^{x} )}^{2} - 90 \times {3}^{x} + 729 = 0$

Now, let

${3}^{x} = y$

Therefore, equation reduces to,

${y}^{2} \: - 90y \: + 729 = 0$

Middle term splitting, -81y, -9y

${y}^{2} - 81y \: - 9y \: + \: 729 \: = 0$

$y(y - 81) \: - 9(y \: - 81) = 0$

$(y \: - \: 81)(y \: - \: 9) \: = \: 0$

$(y \: - 81) = 0 \: \: or \: \: (y \: - \: 9) = 0$

$y \: = 81 \: \: or \: \: y \: \: = 9$

${3}^{x} = 81 \: \: or \: \: {3}^{x \: \: } \: = \: 9$

${3}^{x} = {3}^{4} \: \: or \: {3}^{x \: \: } = \: \: {3}^{2}$

$x = 4 \: \: or \: \: x \: \: = \: 2$

Hence, the answer.