If log_2 x + log_x 2 = frac{10}{3} = log_2 y | vedclass

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(D) Let $t = \log_2 x$. The given equation is $t + \frac{1}{t} = \frac{10}{3}$.Multiplying by $3t$,we get $3t^2 - 10t + 3 = 0$.Factoring the quadratic

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(D) Let $t = \log_2 x$. The given equation is $t + \frac{1}{t} = \frac{10}{3}$.Multiplying by $3t$,we get $3t^2 - 10t + 3 = 0$.Factoring the quadratic,we have $(3t - 1)(t - 3) = 0$.Thus,$t = 3$ or $t = \frac{1}{3}$.Since $x 
eq y$,we assign $\log_2 x = 3$ and $\log_2 y = \frac{1}{3}$ (or vice versa).This gives $x = 2^3 = 8$ and $y = 2^{1/3} = \sqrt[3]{2}$.Therefore,$x + y = 8 + \sqrt[3]{2}$.

If $\log_2 x + \log_x 2 = \frac{10}{3} = \log_2 y + \log_y 2$ and $x \neq y$,then $x + y = $

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