Which of the following statement(s) is (are) true?.... VIDEO
Which of the following statement(s) is (are) true?
(1) If \( a^{x}=b^{y}=c^{z} \) and \( a, b, c \) are in \( G P \), then \( x, y, z \) are in \( H P \).
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(2) If \( a^{1 / x}=b^{1 / y}=c^{1 / z} \) and \( a, b, c \) are in \( G P \), then \( x, y \), \( z \) are in \( A P \).
(3) If \( a, b, c \) are positive, each of them not equal to 1 , and are in \( G P \), then, for any positive \( u \neq 1 \), \( \log _{a} u, \log _{b} u, \log _{c} u \) are in HP.
(4) If \( a, b, c \) are in \( A P \) and \( b, c, a \) are in \( H P \), then \( c \), \( a, b \) are in \( G P \).
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