UrbanPro
true

Take Engineering Entrance Coaching from the Best Tutors

  • Affordable fees
  • 1-1 or Group class
  • Flexible Timings
  • Verified Tutors

Search in

Logarithm with JEE Example

Pulkit
23/05/2018 0 0

JEE 2011 Question on Logarithm

Let (x0,y0) be the solution of the following equations: (2x)ln2 = (3y)ln3 3lnx = 2lny
Then x0 is
(A)
1 6
(B)
1 3
(C)
1 2
(D) 6
Answer and Comments: (C). We can treat the data as a system of equations in the unknowns lnx and lny instead of x and y. This is permissible because a (positive) real number is uniquely determined by its logarithm. So, taking logarithms, we get
(ln2)2 + (ln2)(lnx) = (ln3)2 + (ln3)(lny) (1) (ln3)(lnx) = (ln2)(lny) (2)
which can be treated as a system of linear equations in the unknowns lnx and lny. Eliminating lny from the two equations gives (ln2)3 + (ln2)2(lnx)−(ln3)2(ln2) = (ln3)2(lnx) (3)
5
which simpliï¬?es to [(ln3)2 −(ln2)2](lnx) =−(ln2)[(ln3)2 −(ln2)2] (4) As (ln3)6= ±(ln2), we cancel the bracketed factor and get lnx = −ln2 (5) which gives x = 1/2. Once the key idea strikes, viz. to take lnx and lny as the variables, the problem is straightforward. The properties of logarithms needed are elementary and standard. Nowhere we have to convert logarithms w.r.t. one base to those w.r.t. another.

0 Dislike
Follow 2

Please Enter a comment

Submit

Other Lessons for You

Partnership-Features,Merits,Demerits | Class 12,HSC
Std XIIth OC,Business Studies-Characteristics, Advantages,Disadvantages of Partnership

Difference between Micro and Macro Economics - Class 11/Class 12, HSC, Economics
Difference between Mirco-Economics and Macro-Economics - Std XIth/Std XIIth, Commerce-

Directions Cosines and Directions Ratios (3D GEOMETRY)
Direction Cosines are the Cosines Of the Angles of the angles between and the line and the coordinate Axis. If we have a vector (a,b,c) in space then two a=x2-x1,b=y2-y1 and c =z2-z1 are called the direction...


X

Looking for Engineering Entrance Coaching Classes?

The best tutors for Engineering Entrance Coaching Classes are on UrbanPro

  • Select the best Tutor
  • Book & Attend a Free Demo
  • Pay and start Learning

Take Engineering Entrance Coaching with the Best Tutors

The best Tutors for Engineering Entrance Coaching Classes are on UrbanPro

This website uses cookies

We use cookies to improve user experience. Choose what cookies you allow us to use. You can read more about our Cookie Policy in our Privacy Policy

Accept All
Decline All

UrbanPro.com is India's largest network of most trusted tutors and institutes. Over 55 lakh students rely on UrbanPro.com, to fulfill their learning requirements across 1,000+ categories. Using UrbanPro.com, parents, and students can compare multiple Tutors and Institutes and choose the one that best suits their requirements. More than 7.5 lakh verified Tutors and Institutes are helping millions of students every day and growing their tutoring business on UrbanPro.com. Whether you are looking for a tutor to learn mathematics, a German language trainer to brush up your German language skills or an institute to upgrade your IT skills, we have got the best selection of Tutors and Training Institutes for you. Read more