If $x = {\log _a}(bc),y = {\log _b}(ca),z = {\log _c}(ab),$then which of the following is equal to $1$
If $x = {\log _a}(bc),y = {\log _b}(ca),z = {\log _c}(ab),$then which of the following is equal to $1$
- A
$x + y + z$
- B
${(1 + x)^{ - 1}} + {(1 + y)^{ - 1}} + {(1 + z)^{ - 1}}$
- C
$xyz$
- D
None of these
Similar Questions
If ${\log _k}x.\,{\log _5}k = {\log _x}5,k \ne 1,k > 0,$ then $x$ is equal to
If ${\log _k}x.\,{\log _5}k = {\log _x}5,k \ne 1,k > 0,$ then $x$ is equal to
The value of $6+\log _{\frac{3}{2}}\left(\frac{1}{3 \sqrt{2}} \sqrt{4-\frac{1}{3 \sqrt{2}} \sqrt{4-\frac{1}{3 \sqrt{2}} \sqrt{4-\frac{1}{3 \sqrt{2}} \ldots}}}\right)$ is
The value of $6+\log _{\frac{3}{2}}\left(\frac{1}{3 \sqrt{2}} \sqrt{4-\frac{1}{3 \sqrt{2}} \sqrt{4-\frac{1}{3 \sqrt{2}} \sqrt{4-\frac{1}{3 \sqrt{2}} \ldots}}}\right)$ is
- [IIT 2012]
If ${\log _4}5 = a$ and ${\log _5}6 = b,$ then ${\log _3}2$ is equal to
If ${\log _4}5 = a$ and ${\log _5}6 = b,$ then ${\log _3}2$ is equal to
If $\log x:\log y:\log z = (y - z)\,:\,(z - x):(x - y)$ then
If $\log x:\log y:\log z = (y - z)\,:\,(z - x):(x - y)$ then
${\log _7}{\log _7}\sqrt {7(\sqrt {7\sqrt 7 } )} = $
${\log _7}{\log _7}\sqrt {7(\sqrt {7\sqrt 7 } )} = $