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if a>0 , a is not equal to 1 then 2logxa+logaxa+3loga2xa=0 has 1 exactly one root 2 two real root 3 no real root 4 infinite many root

if a>0 , a is not equal to 1 then 2logxa+logaxa+3loga2xa=0 has
1 exactly one root
2 two real root
3 no real root
4 infinite many root

Grade:11

1 Answers

Vikas TU
14149 Points
7 years ago
2logxa+logaxa+3loga2xa=0
can be written as: {by applying property}
=> log(x^2*ax*(a^2x)^3) = 0 {base a}
=>  x^2*ax*(a^2x)^3 = 1
=> x^6*a^7 = 1
=> x^6 = 1/a^7
or
x^6 – 1/a^7 = 0
it will have maximum 6 roots as it is the sixth power of x.

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