If ${\log _5}a \cdot {\log _a}x = 2$,then the value of $x$ is:

The number of real values of the parameter $k$ for which the equation $(\log_{16} x)^2 - \log_{16} x + \log_{16} k = 0$ has exactly one real solution is:

If $m^n = n^m$,then the value of $m$ in terms of $n$ is:

$7\log \left( \frac{16}{15} \right) + 5\log \left( \frac{25}{24} \right) + 3\log \left( \frac{81}{80} \right) =$

If ${\log _{0.3}}(x - 1) < {\log _{0.09}}(x - 1)$,then $x$ lies in which interval?

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