Question

# 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:

A
A.P.
B
G.P.
C
H.P.
D
none of these

Solution

## The correct option is A A.P.$$x_{1}, y_{1}, z \rightarrow G \cdot Y$$$$y^{2}=x \times z$$taking log both sides$$\ln y^{2}=\ln (x \times z)$$$$2 \ln y=\ln x+\ln z$$$$2(1+\ln y)=(1+\ln x)+(1+\ln z)$$$$\therefore \quad 1+\ln x, \quad 1+\ln y, \quad 1+\ln z$$ are in $$AP$$Hence $$\dfrac{1}{1+\ln x}, \dfrac{1}{1+\ln y}, \dfrac{1}{1+\ln z}$$ are in H.P.Maths

Suggest Corrections

0

Similar questions
View More

People also searched for
View More