If ${{\log x} \over {b - c}} = {{\log y} \over {c - a}} = {{\log z} \over {a - b}},$ then which of the following is true
$xyz = 1$
${x^a}{y^b}{z^c} = 1$
${x^{b + c}}{y^{c + a}}{z^{a + b}} = 1$
All of These
The sum of all the natural numbers for which $log_{(4-x)}(x^2 -14x + 45)$ is defined is -
For $y = {\log _a}x$ to be defined $'a'$ must be
Let $a=3 \sqrt{2}$ and $b=\frac{1}{5^{\frac{1}{6}} \sqrt{6}}$. If $x, y \in R$ are such that $3 x+2 y=\log _a(18)^{\frac{5}{4}} \text { and }$ $2 x-y=\log _b(\sqrt{1080}),$ then $4 x+5 y$ is equal to. . . .
The solution of the equation ${\log _7}{\log _5}$ $(\sqrt {{x^2} + 5 + x} ) = 0$
If $x = {\log _5}(1000)$ and $y = {\log _7}(2058)$ then