If $x = {\log _a}(bc),y = {\log _b}(ca),z = {\log _c}(ab),$then which of the following is equal to $1$
$x + y + z$
${(1 + x)^{ - 1}} + {(1 + y)^{ - 1}} + {(1 + z)^{ - 1}}$
$xyz$
None of these
If $\log x:\log y:\log z = (y - z)\,:\,(z - x):(x - y)$ then
If $x = {\log _b}a,\,\,y = {\log _c}b,\,\,\,z = {\log _a}c$, then $xyz$ is
If ${\log _{10}}x = y,$ then ${\log _{1000}}{x^2} $ is equal to
The sum $\sum \limits_{n=1}^{\infty} \frac{2 n^2+3 n+4}{(2 n) !}$ is equal to :
$\sum\limits_{r = 1}^{89} {{{\log }_3}(\tan \,\,{r^o})} = $