The sum of the solution of the equation $9^{x} - {6.3}^{x} + 8 = 0$ is

{log}_{3} 2

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{log}_{3} 6

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{log}_{3} 8

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{log}_{3} 4

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Solution

The correct option is D ${log}_{3} 8$
$9^{x} - {6.3}^{x} + 8 = 0 ⟹ (3^{x})^{2} - 6 (3^{x}) + 8 = 0 ⟹ 3^{x} = 2, 4 ⟹ x = {log}_{3} 2, {log}_{3} 4$
Sum of roots is ${log}_{3} 2 + {log}_{3} 4 = {log}_{3} 8$

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