Question

Given that $a^x=b^y=c^z=d^u$ & a, b, c, d are in GP, then x, y, z, u are in...

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

Answer 1

The correct option is C $HP$

Given $a,b,c,d$ are in GP.
Then $b=ar,c=a{r}^2,d=a{r}^3$
$a^x=b^y=c^z=d^u$
Taking log on both sides
$x\log a=y\log ar=z\log a{r}^2=u\log a{r}^3=\lambda$
$\Rightarrow \frac{\lambda }{x}=\log a,\frac{\lambda }{y}=logar,\frac{\lambda }{z}=loga{r}^2,\frac{\lambda }{u}=loga{r}^3$