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Question 8: logxy + logyx2 = 3. Find logxy3.
logxy + logyx2 = 3
Let a = logxy
logx3 = \\frac{1}{log_3{x}}\\)
logyx2 = 2logyx
We know that logyx = \\frac{1}{log_x{y}}\\)
Hence form above logyx = \\frac{1}{a}\\)
Now rewritting the equation logxy + logyx2 = 3
Using a we get a + \\frac{2}{a}\\) = 3
i.e., a2 - 3a + 2 = 0
Solving we get a = 2 or 1
If a = 2, Then logxy = 2 and logyx3 = 3
logxy = 3 * 2 = 6
Or
If a = 1, Then logxy = 1 and logyx3 = 3
logxy = 3 * 1 = 3
The question is "Find logxy3."
Choice B is the correct answer.
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