$\log ab - \log |b| = $

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?

If $3^x=4^{x-1}$, then $x=$

$(A)$ $\frac{2 \log _3 2}{2 \log _3 2-1}$ $(B)$ $\frac{2}{2-\log _2 3}$ $(C)$ $\frac{1}{1-\log _4 3}$ $(D)$ $\frac{2 \log _2 3}{2 \log _2 3-1}$

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

If ${\log _{10}}3 = 0.477$, the number of digits in ${3^{40}}$ is

${\log _7}{\log _7}\sqrt {7(\sqrt {7\sqrt 7 } )} = $