If $\log _{10} 7 = 0.8451$,then the position of the first significant figure of $7^{-20}$ is

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

The sum of the roots of the equation $x+1-2 \log _{2}\left(3+2^{x}\right)+2 \log _{4}\left(10-2^{-x}\right)=0$ is:

If $n = (2020)!$,then the value of $\frac{1}{\log _{2} n} + \frac{1}{\log _{3} n} + \frac{1}{\log _{4} n} + \ldots + \frac{1}{\log _{2020} n}$ is equal to:

If $a^x = b^y = c^z = d^w$,the value of $x\left(\frac{1}{y} + \frac{1}{z} + \frac{1}{w}\right)$ is

If $\alpha = \log_e(2+\sqrt{3})$,then $\frac{\cosh \alpha}{1-\tanh \alpha} + \frac{\sinh \alpha}{1-\coth \alpha} = $