wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Let x,xlog10x,ylog10y and (xy)log10(xy) are four consecutive terms of a geometric progression (x, y > 0).

Number of ordered pair (x, y) is


A

2

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

3

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

4

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

more than four

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

The correct option is B

3


If a, b, c, d are four terms in G.P. then loga, logb, logc and logd are in A.P.
log10x,log210x,log210y,log210(xy), in A.P.
log210(xy),log210ylog210x, (i)
Also log210ylog210x,=log210xlog210x, (2)
form(1)
(log10x+log10y)(log10xlog10y)=log210ylog210x(log10x+2log10y)(log10x)=log210ylog210xlog210y2log10y.log10x2log210x=0 (3)from(2)
log210y2log210x+log10x=0 (4)(3)(4)2log10y.log10xlog10x=0 x=1 or y=110
Now, if x=1y=1
Also, if x=1y=1
Also, if y=1102log210x=log10x14=0
logx10x=1±1+24=1±34x=x1±34=1±34
x=x1±34(1,1),(101+34,110)(10134,110) are three ordered pair


flag
Suggest Corrections
thumbs-up
3
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Inverse of a Function
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon