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

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

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

Similar Questions

A number is the reciprocal of the other. If the arithmetic mean of the two numbers be $\frac{{13}}{{12}}$, then the numbers are

The sum of the integers from $1$ to $100$ which are not divisible by $3$ or $5$ is

Insert $6$ numbers between $3$ and $24$ such that the resulting sequence is an $A.P.$

If ${a_1},\,{a_2},....,{a_{n + 1}}$ are in $A.P.$, then $\frac{1}{{{a_1}{a_2}}} + \frac{1}{{{a_2}{a_3}}} + ..... + \frac{1}{{{a_n}{a_{n + 1}}}}$ is

Find the sum of all natural numbers lying between $100$ and $1000,$ which are multiples of $5 .$