Home
Class 12
MATHS
If x gt 1, y gt 1, z gt 1 are in G.P., t...

If `x gt 1`, `y gt 1`, `z gt 1` are in `G.P.`, then `log_(ex)e`, `log_(ey)e` , `log_(ez)e` are in

A

`A.P.`

B

`H.P.`

C

`G.P.`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B

`(b)` Let `x=e`, `y=e^(2)`, `z=e^(3)`
`:.` Given terms are `log_(e^(2))e`, `log_(e^(3))e`, `log_(e^(4))e`
or `(1)/(2),(1)/(3),(1)/(4)` which are in `H.P.`
Promotional Banner

Topper's Solved these Questions

  • PROGRESSION AND SERIES

    CENGAGE|Exercise Comprehension|7 Videos
  • PROGRESSION AND SERIES

    CENGAGE|Exercise Multiple Correct Answer|4 Videos
  • PROBABILITY II

    CENGAGE|Exercise JEE Advanced Previous Year|25 Videos
  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise JEE Advanced Previous Year|11 Videos

Similar Questions

Explore conceptually related problems

If x gt 1, y gt 1, z gt 1 are in G.P then 1/(1 + log x),1/(1 + log y),1/(1 + log z) are in

17. If x gt 1, y gt 1, z gt1 are in G.P, then 1/(1+ ln x), 1/( 1+ ln y), 1/(1+ lnz) are in

If x,y,z are in G.P. (x,y,z gt 1) , then (1)/(2x+log_(e)x) , (1)/(4x+log_(e)y) , (1)/(6x+log_(ez)z) are in

If a >1,b >1 and c >1 are in G.P. then show that 1/(1+(log)_e a),1/(1+(log)_e b), a n d1/(1+(log)_e c) are in H.P.

Evaluate: int(log_(e x)e*log_(e^2x)e*log_(e^3x)e)/x dx

If x gt 0 , y gt 0 , z gt 0 , the least value of x^(log_(e)y-log_(e)z)+y^(log_(e)z-log_(e)x)+Z^(log_(e)x-log_(e)y) is

I=int \ log_e (log_ex)/(x(log_e x))dx

If log_(e)4 = 1.3868 , then log_(e) 4.01 =

If f(x)=log_(e)(log_(e)x)/log_(e)x then f'(x) at x = e is

Prove that log_(e)(1+x)ltxforxgt0