MCQ
If ${\log _x}a,\;{a^{x/2}}$ and ${\log _b}x$ are in $G.P.$, then $x = $
- A$ - \log ({\log _b}a)$
- B$ - {\log _a}({\log _a}b)$
- ✓${\log _a}({\log _e}a) - {\log _a}({\log _e}b)$
- D${\log _a}({\log _e}b) - {\log _a}({\log _e}a)$
$ \Rightarrow $${a^x} = {\log _b}a$
$ \Rightarrow $$x = {\log _a}({\log _b}a)$
$ \Rightarrow $$x = {\log _a}\left( {\frac{{{{\log }_e}a}}{{{{\log }_e}b}}} \right) = {\log _a}({\log _e}a) - {\log _a}({\log _e}b)$.
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