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

The product of all positive real values of $x$ satisfying the equation $x^{\left(16\left(\log _5 x\right)^3-68 \log _5 x\right)}=5^{-16}$is. . . . .

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

The value of $\sqrt {(\log _{0.5}^24)} $ is

If $x = {\log _3}5,\,\,\,y = {\log _{17}}25,$ which one of the following is correct

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

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