Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

In the graph of \(y = a^x\) you can see at only one point the value of the y = 1. That is at x = 0. At no other value between - infinity and + infinity the value of y becomes 1. It's an always increasing curve. Irrational value also lie between - infinity and + infinity . Hence at no other irrational value is y = 1.
_________________

The question is not can you rise up to iconic! The real question is will you ?

Hi Instructors, Request you to please clarify the below doubt on the usage of the property

\(x^y\) = 1

If X is not equal to 0 and\(x > 1\); Will the value of y be always 0. I mean, isnt it possible that y has some irrational value that makes \(x^y\) = 1

Example; \(2^(1/irrational value) = 1\). If not, what can we infer about the value of whole expression if \(x^(1/irrational value)\)

A number that can be expressed as a ratio of two numbers is rational. However, roots, \(\pi\), and endless non-repeating decimals are irrational numbers; they cannot be written in a ratio of two numbers. Moreover, an infinite amount of irrational numbers exist between integers. But, in no way, there is an infinite amount of irrational numbers that make integers, applying the logic that you used above.

I believe you are thinking as if rational and irrational numbers acted like odd and even numbers. Even though O + O = E or O + E = O, no such relationship exists between rational and irrational numbers.

I hope this helps.

gmatclubot

Re: Concept Clarity on X^y =1
[#permalink]
04 Jun 2013, 21:00

There’s something in Pacific North West that you cannot find anywhere else. The atmosphere and scenic nature are next to none, with mountains on one side and ocean on...

This month I got selected by Stanford GSB to be included in “Best & Brightest, Class of 2017” by Poets & Quants. Besides feeling honored for being part of...

Joe Navarro is an ex FBI agent who was a founding member of the FBI’s Behavioural Analysis Program. He was a body language expert who he used his ability to successfully...