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# What is the value of log

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Let x and y be two positive real numbers such that: log_x  y+log_y  x = 3

Find the value of: log_x  y^2 + log_y  x^2

Feb 22, 2019

$$\log_x(y^2) + \log_y(x^2) = \\ 2 \log_x(y) + 2\log_y(x) = \\ 2( \log_x(y) + \log_y(x) ) = \\ 2 \cdot 3 = 6$$