if a^x= b^y = (ab)^(xy) prove that x+y =1

ln(a^x) = ln(b^y) = ln((ab)^(xy))
xln(a) = xyln(ab)
ln(a) = yln(ab) = y(ln(a) + ln(b))
y = ln(a)/(ln(a)+ln(b))
with same analysis for ln(b^y):
ln(b) = x(ln(a) + ln(b))x = ln(b)/(ln(a)+ln(b))
x + y = (ln(a) + ln(b))/(ln(a) + ln(b)) = 1

Answered by Scott C. Maths tutor

5096 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Where do the graphs of y=3x-2 and y=x^2+4x-8 meet?


How to find the derivative of arctan(x)


How do you find the coordinates of stationary points on a graph?


Solve for -pi < x < pi: tanx = 4cotx + 3


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