Question

Please solve question number 12

Answer 1

${a}^{x} = {b}^{y} = {c}^{z} = k(let) \\ log \: a = \frac{1}{x} logk \\ log \: b = \frac{1}{y} logk \\ logc = \frac{1}{z} logk \\ \\ \frac{log \: a \: logc}{ {(logb)}^{2} } \\ = \frac{ \frac{1}{x} logk \: \frac{1}{z} logk}{ \frac{1}{ {y}^{2} }(logk ){}^{2} } \\ = \frac{ \frac{1}{x} \frac{1}{z} }{ \frac{1}{ {y}^{2} } } \\ = \frac{ {y}^{2} }{xz}....(1) \\ \\ since \: \: y = \sqrt{xz} \\ {y}^{2} = xz.....(2) \\ \\ from \: (1) \: and \: (2) \\ ans \: is \: 1 \\ \\ = 1$


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