જો $x = {\log _a}(bc),y = {\log _b}(ca),z = {\log _c}(ab),$ તો આપેલ પૈકી કોની કિમત $1$ છે.
Medium
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b
(b) \(x = {\log _a}bc\) \( \Rightarrow \) \(1 + x = {\log _a}a + {\log _a}bc = {\log _a}abc\)
(b) \(x = {\log _a}bc\) \( \Rightarrow \) \(1 + x = {\log _a}a + {\log _a}bc = {\log _a}abc\)
\(\therefore {(1 + x)^{ - 1}} = {\log _{abc}}a\)
\(\therefore {(1 + x)^{ - 1}} + {(1 + y)^{ - 1}} + {(1 + z)^{ - 1}} = {\log _{abc}}a + {\log _{abc}}b + {\log _{abc}}c\)
\( = {\log _{abc}}abc = 1\).
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