Simplify ln(e^2) - 4ln(1/e)

Using log rules, we can simplify the equation as follows: Firstly log(xa) = alog(x) implies that ln(e2) = 2ln(e). Next loga(a) = 1 implies 2ln(e) = 21 = 2 [Since the natural logarithm ln is equivalent to loge]. So ln(e2) = 2. Following this ln(1/e) = ln(e-1), which from the previous rule we can see ln(e-1) = -ln(e). Lastly we know ln(e) = 1, so -4*-ln(e) = -4*-1 = 4. So -4ln(1/e) = 4. Therefore ln(e2) - 4ln(1/e) = 2 + 4 = 6

MJ
Answered by Mark J. Maths tutor

4982 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

The points A and B have coordinates (1, 6) and (7,− 2) respectively. (a) Find the length of AB.


Find the roots of the equation y=x^2-8x+5 by completing the square.


Find the coordinates of the stationary points y=x^4-8x^2+3


Differentiate y = lnx + 4x^2 + 3e^4x with respect to x


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning