If ${\log _x}a,\;{a^{x/2}}$ and ${\log _b}x$ are in $G.P.$, then $x = $
$ - \log ({\log _b}a)$
$ - {\log _a}({\log _a}b)$
${\log _a}({\log _e}a) - {\log _a}({\log _e}b)$
${\log _a}({\log _e}b) - {\log _a}({\log _e}a)$
The sum to infinity of the progression $9 - 3 + 1 - \frac{1}{3} + .....$ is
Find the sum to indicated number of terms in each of the geometric progressions in $\left.1,-a, a^{2},-a^{3}, \ldots n \text { terms (if } a \neq-1\right)$
Find the $12^{\text {th }}$ term of a $G.P.$ whose $8^{\text {th }}$ term is $192$ and the common ratio is $2$
$\alpha ,\;\beta $ are the roots of the equation ${x^2} - 3x + a = 0$ and $\gamma ,\;\delta $ are the roots of the equation ${x^2} - 12x + b = 0$. If $\alpha ,\;\beta ,\;\gamma ,\;\delta $ form an increasing $G.P.$, then $(a,\;b) = $
$0.14189189189….$ can be expressed as a rational number