Question

solve log(base √z) x × log(base√x) y × log(base √y) z​

Answer 1

Answer:

$given \: that \\ \\ log_{ \sqrt{z} }(x) \: \times log_{ \sqrt{x} }(y) \: \times log_{ \sqrt{y} }(z) \\ \\ = log_{ {z}^{ \frac{1}{2} } }(x) \: \times log_{ {x}^{ \frac{1}{2} } }(y) \: \times log_{ {y}^{ \frac{1}{2} } }(z) \\ \\ = \frac{1}{ \frac{1}{2} } log_{z}(x) \times \frac{1} { \frac{1}{2} } log_{x}(y) \times \frac{1}{ \frac{1}{2} } log_{y}(z) \\ \\ = 2 \frac{ log(x) }{ log(z) } \times 2 \frac{ log(y) }{ log(x) } \times 2 \frac{ log(z) }{ log(y) } \\ \\ = 8 \: ans. \\ \\ \: formula \: used \: are \: log_{n}(m) = \frac{ log(m) }{ log(n) } \\ \\ and log_{ {m}^{n} }(p) = \frac{1}{n} log_{m}(p)$