The value of ${(0.05)^{{{\log }_{_{\sqrt {20} }}}(0.1 + 0.01 + 0.001 + ......)}}$ is

If ${1 \over 2} \le {\log _{0.1}}x \le 2$ then

Let $n$ be the smallest positive integer such that $1+\frac{1}{2}+\frac{1}{3}+\ldots+\frac{1}{n} \geq 4$. Which one of the following statements is true?

For $y = {\log _a}x$ to be defined $'a'$ must be

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 value of ${81^{(1/{{\log }_5}3)}} + {27^{{{\log }_{_9}}36}} + {3^{4/{{\log }_{_7}}9}}$ is equal to