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The real number \(x\) satisfies \(2^{\log_x 7} = 49^{\log_2 x}.\)

 

Find \((\log_2 x)^2.\)

 Apr 13, 2020
 #1
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\(2^{\log_x 7} = 49^{\log_2 x}\\ log_2(2^{\log_x 7}) = log_2(49^{\log_2 x})\\ log_x7=log_2x*log_249\\ \frac{log_27}{log_2x}=2log_2x*log_27\\ \frac{1}{log_2x}=2log_2x\\ \frac{1}{2}=(log_2x)^2\\ (log_2x)^2=\frac{1}{2} \)

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 Apr 13, 2020

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