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zmudz
 one year ago
Suppose \(A\) and \(B\) are positive real numbers for which \(\log_A B = \log_B A\). If neither \(A\) nor \(B\) is 1 and \(A \neq B\), find the value of \(AB\).
zmudz
 one year ago
Suppose \(A\) and \(B\) are positive real numbers for which \(\log_A B = \log_B A\). If neither \(A\) nor \(B\) is 1 and \(A \neq B\), find the value of \(AB\).

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ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2let \[\log_AB = \log_B A = k\] \(\implies B = A^k ~~\text{and} ~~A = B^k\tag{1}\) \(\implies AB = A^kB^k=(AB)^k\) \(\implies AB=1\) or \(k=1\) however\(k=1\) is impossible because it gives \(A=B\) from \((1)\)
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