Find the exact solutions, in their simplest form, to the equations : a) 2ln(2x + 1)-4=0 b)7^(x)e^(4x)=e^5

a) 2ln(2x + 1)-4=0

-> ln(2x + 1)-2=0

-> ln(2x + 1)=2

-> (2x + 1)=e2

-> 2x = e-1

-> x = (e-1)/2

b) 7xe4x=e5

-> 7x=e\ e4x

​​​​​​​-> 7x=e5-4x

​​​​​​​-> ln(7x)=5-4x

​​​​​​​-> xln(7)=5-4x

​​​​​​​-> x(ln(7)+4)=5

​​​​​​​-> x=5/(ln(7)+4)

EL
Answered by Elizabeth L. Maths tutor

4313 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Differentiate (2^x)(5x^2+5x)^2.


integrate 1/(x^2+4x+13)


If y = 2^x, solve the equation 8(4^x) + 9(2^x) + 1 = 0 in terms of y.


Calculate the integral of ln(x)


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