What is greater e^pi or pi^e?

Let a^b >b^a, then blna>alnb, (lna)/a > (lnb)/b, Thus we graph the function (lnx)/x, We can see that this tends towards 0 as x tends towards infinity. We can also see that it is increasing from x=0 to a certain value of x. We can then find the maximum value of our function by finding the derivative. By using the product rule and setting our derivative to 0, we find x=e. Therefore (lne)/e>(lnb)/b for any b>0. Thus blne>elnb, e^b>b^e e^pi>pi^e

QED

Related Maths A Level answers

All answers ▸

What is the chain rule and how is it used?


Is a line ax+by+c=0 tangent to a circle?


Differentiate x^2+4x+9.


A curve is defined by the equation y^2 - xy + 3x^2 - 5 = 0. Find dy/dx.


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences