If x -1- y -1- z -1 are in GP- then 1-1-ln x- 1-1-ln y - 1-1-ln z are inA- APB- HPC- GPD- None of these

The correct option is B HP Let the common ratio of the GP be r. Then, y=xr and z =xr^2 ⇒ ln y = ln x+ln r and ln z = ln x+2 ln r Let A = 1 + ln x, D = ln r ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard X

Mathematics

Sum of Infinite Terms

If x >1, y >1...

Question

If $x > 1, y > 1, z > 1$ are in GP, then $\frac{1}{1 + l n x}, \frac{1}{1 + l n y}, \frac{1}{1 + l n z}$ are in

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

None of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B
HP

Let the common ratio of the GP be r. Then,
$y = x r$ and $z = x r^{2}$
$\Rightarrow l n y = l n x + l n r$ and $l n z = l n x + 2 l n r$
Let $A = 1 + l n x, D = l n r$
Then, $\frac{1}{1 + l n x} = \frac{1}{A}, \frac{1}{1 + l n y} = \frac{1}{1 + l n x + l n r} = \frac{1}{A + D}$
and $\frac{1}{1 + l n z} = \frac{1}{1 + l n x + 2 l n r} = \frac{1}{A + 2 D}$
Therefore, $\frac{1}{1 + l n x}, \frac{1}{1 + l n y}, \frac{1}{1 + l n z}$ are in HP

Suggest Corrections

Similar questions

Q. If

x > 1, y > 1, z > 1

are in GP, then

\frac{1}{1 + l n x}, \frac{1}{1 + l n y}, \frac{1}{1 + l n z}

are in

Q. If

x > 1, y > 1, z > 1

are in GP, then

\frac{1}{1 + l n x}, \frac{1}{1 + l n y}, \frac{1}{1 + l n z}

are in

Q. If

x > 1, y > 1, z > 1

are three numbers in GP then

\frac{1}{1 + ln x}

\frac{1}{1 + ln y}

\frac{1}{1 + ln z}

are in

Q. If x > 1, y > 1, z >1 are in G.P., then

\frac{1}{1 + l n x}, \frac{1}{1 + l n y}, \frac{1}{1 + l n z}

are in

Q. If

x > 1, y > 1, z > 1

are in G.P. Then

\frac{1}{1 + ln x}, \frac{1}{1 + ln y}, \frac{1}{1 + ln z}

are in:

Join BYJU'S Learning Program

If x>1,y>1,z>1 are in GP, then 11+ln x,11+ln y,11+ln z are in

The correct option is B HP Let the common ratio of the GP be r. Then, y=xr and z=xr2 ⇒ln y=ln x+ln r and ln z=ln x+2 ln r Let A=1+ln x, D=ln r Then, 11+ln x=1A,11+ln y=11+ln x+ln r=1A+D and 11+ln z=11+ln x+2 ln r=1A+2D Therefore, 11+ln x,11+ln y,11+ln z are in HP

If $x > 1, y > 1, z > 1$ are in GP, then $\frac{1}{1 + l n x}, \frac{1}{1 + l n y}, \frac{1}{1 + l n z}$ are in