If `(log)_x a , a^(x//2) and (log)_b x` are in G.P., then write the value of `x`
(a)`log a (log_b a)`
(b) `log a (log_e a) – loga (log_e b)`
(c) `–log a (log_a b)`
(d) none of these

Explanation

`log_x ^a ,a^(x//2) and log_b x`
are in G.P.

Then

`(a^(x/2))^2=log_b x xx log_x a`

`a^x=(log x)/(log b)xx(log a)/(log x)`

`a^x=(log a)/(log b)`

as `xloga=log[loga]−log(logb)`

`implies (log(log a)-log(log b))/(log a)`

...