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;

DS
Answered by Daljit S. Maths tutor

8254 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

what is d(2x^3)/dx?


How do we differentiate y = arctan(x)?


How do I write the function 3cosθ+4sinθ in the form Rsin(θ + α), where R and α are positive constants?


If y = 5x^3 - 2x^2 + 2, what is 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