If log _e mathrm{a}, log _e mathrm{~b}, log _ | vedclass

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Question

$\log _e a, \log _e b, \log _e c$ are in $ A.P.$

$	herefore \mathrm{b}^2=\mathrm{ac}$

Also

$\log _{\circ}\left(\frac{a}{2 b}ight), \log _{

Vedclass · Accepted Answer

$9: 6: 4$

Vedclass · Answer

$\log _e a, \log _e b, \log _e c$ are in $ A.P.$

$	herefore \mathrm{b}^2=\mathrm{ac}$

Also

$\log _{\circ}\left(\frac{a}{2 b}ight), \log _{\circ}\left(\frac{2 b}{3 c}ight), \log _{\circ}\left(\frac{3 c}{a}ight)$ are in $A.P.$

$\left(\frac{2 b}{3 \mathrm{c}}ight)^2=\frac{\mathrm{a}}{2 \mathrm{~b}} 	imes \frac{3 \mathrm{c}}{\mathrm{a}} $

$ \frac{\mathrm{b}}{\mathrm{c}}=\frac{3}{2}$

Putting in eq. $(i)$ $b^2=a 	imes \frac{2 b}{3}$

$ \frac{a}{b}=\frac{3}{2}$

$ a: b: c=9: 6: 4$

If $\log _e \mathrm{a}, \log _e \mathrm{~b}, \log _e \mathrm{c}$ are in an $A.P.$ and $\log _e \mathrm{a}-$ $\log _e 2 b, \log _e 2 b-\log _e 3 c, \log _e 3 c-\log _e a$ are also in an $A.P,$ then $a: b: c$ is equal to

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