If ${a^x} = b,{b^y} = c,{c^z} = a,$ then value of $xyz$ is
$0$
$1$
$2$
$3$
Let $a , b , c$ be three distinct positive real numbers such that $(2 a)^{\log _{\varepsilon} a}=(b c)^{\log _e b}$ and $b^{\log _e 2}=a^{\log _e c}$. Then $6 a+5 b c$ is equal to $........$.
The interval of $x$ in which the inequality ${5^{(1/4)(\log _5^2x)}}\, \geqslant \,5{x^{(1/5)(\log _5^x)}}$
The number ${\log _2}7$ is
If $\log x:\log y:\log z = (y - z)\,:\,(z - x):(x - y)$ then
The sum $\sum \limits_{n=1}^{\infty} \frac{2 n^2+3 n+4}{(2 n) !}$ is equal to :