If x, y, z all are greater than unity and are in G.P., then (1/1 + log x), (1/+ 1 log y), (1/1 + log z) are in

Question

If x, y, z all are greater than unity and are in G.P., then (1/1 + log x), (1/+ 1 log y), (1/1 + log z) are in (A) H.P. (B) GP. (C) A.P. (D) None of these

Tardigrade Admin · Accepted Answer

As x, y, z∈ G.P. ⇒ log x, log y, log z ∈ A.P. or 1 + log x, 1+ log y, 1 +log z ∈ A.P. or (1/1 + log x), (1/+ 1 log y), (1/1 +log z) ∈ H.P.

Q. If $x, y, z$ all are greater than unity and are in $G . P$ ., then $\frac{1}{1 + l o gx}, \frac{1}{+ 1 l o g y}, \frac{1}{1 + l o g z}$ are in

$H . P$ .

$GP$ .

$A . P$ .

None of these

As $x, y, z \in G . P$ .
$\Rightarrow l o gx, l o g y, l o g z \in A . P$ .
or $1 + l o gx, 1 + l o g y, 1 + l o g z \in A . P$ .
or $\frac{1}{1 + l o gx}, \frac{1}{+ 1 l o g y}, \frac{1}{1 + l o g z} \in H . P .$

Q. If x,y,z all are greater than unity and are in G.P., then 1+logx1​,+1logy1​,1+logz1​ are in

H.P.

GP.

A.P.