Find the best tutors and institutes for Engineering Entrance Coaching

Find Best Engineering Entrance Coaching classes

Please select a Category.

Please select a Locality.

No matching category found.

No matching Locality found.

Outside India?

Search for topics

Logarithm with JEE Example

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
1 6
1 3
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)
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


Other Lessons for You

Economics learning made easy
I am an educator of economics for 3 years now teaching students from classes 9 to 12.I am currently working in chegg india as a verified expert in Economics and providing solutions to problems related...

Meaning and Features of Microeconomics - Class 11/12, HSC
What is Microeconomics and what are its features?

Rajiv Vadera | 13 Sep

0 0

How pass a Journal Entry-Class 11, Book-Keeping and Accountancy
Transaction - Started Business with Cash

Rajiv Vadera | 11 Sep

0 0

Chemical Bonding Board Subjective Exercise
Very Short Answer Type Questions : Q.1 I3– is known but F3– is not why? Q.2 Define bond order. Q.3 Define resonance. Q.4 Explain the significance of formal charge. Q.5 Give one example...

Find Best Engineering Entrance Coaching classes?

Find Now » is India's largest network of most trusted tutors and institutes. Over 25 lakh students rely on, to fulfill their learning requirements across 1,000+ categories. Using, parents, and students can compare multiple Tutors and Institutes and choose the one that best suits their requirements. More than 6.5 lakh verified Tutors and Institutes are helping millions of students every day and growing their tutoring business on 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