Solve for x log2 x + log4 x + log8 x =11/6

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We have to solve for x: log2 x + log4 x + log8 x =11/6

log (a) b = 1/ log (b) a

log2 x + log4 x + log8 x =11/6

=> 1 / log(x) 2 + 1 / log(x) 4 + 1/log(x) 2 = 11/6

=> 1 / log(x) 2 + 1 / 2*log(x) 2 + 1/3*log(x) 2 = 11/6

let log(x) 2 = y

=> 1/y + 1/2y + 1/3y = 11/6

=> 6/6y + 3/6y + 2/6y = 11/6

=> 11/6y = 11/6

=> y = 1

So log(x) 2 = 1

=> 2 = x^1

=> x = 2

Therefore x = 2

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