Solve 8(4^x ) – 9(2^x ) + 1 = 0

At first this equation seems tricky, but we can perform a clever substitution to simplify it. We notice that if let y = 2^x, then we can rewrite this as:

8(y^2) - 9y + 1 = 0

This now becomes a simple quadratic equation, which can be simplified to: (8y -1) (y-1) = 0

Therefore y = 1/8; y =1. Now solving for x: 2^x = 1/8 leads to x = -3; 2^x = 1 leads to x = 0;

Answered by Daljit S. Maths tutor

8081 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find the coordinates of the turning points of the curve y = 4/3 x^3 + 3x^2-4x+1


Express Cosx-3Sinx in form Rcos(x+a) and show that cosx-3sinx=4 has no solution MEI OCR June 2016 C4


Differentiate xcos(x) with respect to x.


Find the coordinates of the stationary point on the curve y=2x^2+3x+4=0


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