If $x = {\log _a}(bc),y = {\log _b}(ca),z = {\log _c}(ab),$then which of the following is equal to $1$
$x + y + z$
${(1 + x)^{ - 1}} + {(1 + y)^{ - 1}} + {(1 + z)^{ - 1}}$
$xyz$
None of these
${\log _7}{\log _7}\sqrt {7(\sqrt {7\sqrt 7 } )} = $
The number of solution $(s)$ of the equation $log_7(2^x -1) + log_7(2^x -7) = 1$, is -
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
If $3^x=4^{x-1}$, then $x=$
$(A)$ $\frac{2 \log _3 2}{2 \log _3 2-1}$ $(B)$ $\frac{2}{2-\log _2 3}$ $(C)$ $\frac{1}{1-\log _4 3}$ $(D)$ $\frac{2 \log _2 3}{2 \log _2 3-1}$