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Maths-

General

Easy

Question

Product of roots of the equation $fraction numerator log subscript 8 end subscript invisible function application open parentheses 8 divided by x to the power of 2 end exponent close parentheses over denominator open parentheses log subscript 8 end subscript invisible function application x close parentheses to the power of 2 end exponent end fraction equals 3$ is

1
$1 / 2$
$1 / 3$
$1 / 4$

The correct answer is: $1 divided by 4$

Let $log subscript 8 end subscript invisible function application x equals y comma$ then the given equation reduces to $open parentheses 1 minus 2 y close parentheses divided by y to the power of 2 end exponent equals 3.$
$rightwards double arrow 3 y to the power of 2 end exponent plus 2 y minus 1 equals 0 rightwards double arrow 3 y to the power of 2 end exponent plus 3 y minus y minus 1 equals 0$
$rightwards double arrow 3 y open parentheses y plus 1 close parentheses minus 1 open parentheses y plus 1 close parentheses equals 0 rightwards double arrow log subscript 8 end subscript invisible function application x equals y equals 1 divided by 3 comma blank minus 1$
$rightwards double arrow x equals 2 comma blank 1 divided by 8$

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