Question

If $a,b,c$ are in GP and $a^x=b^y=c^z$, then $x,y,z$ will be in.

• A. AP
• B. GP
• C. HP
• D. None of these

Answer 1

The correct option is C HP

Given $a,b,cϵ$ G.P

$b^2=ac$

Taking $\log$ we get, $2\log b=\log a+\log c..\left(1\right)$

Also given, $a^x=b^y=c^z$

or $x\log a=y\log b=z\log c=k\left(say\right)$

Now using (1), we get

$2.\frac{k}{y}=\frac{k}{x}+\frac{k}{z}$

$\Rightarrow \frac{2}{y}=\frac{1}{x}+\frac{1}{z}$

$\Rightarrow x,y,zϵ$ H.P

Hence, option 'C' is correct.