Hey there! Sign in to join this conversationNew here? Join for free
x Turn on thread page Beta
    • Thread Starter
    Offline

    10
    ReputationRep:
    Name:  Screenshot_45.png
Views: 15
Size:  20.6 KB
    How does e^2ln(2x) simplify to (2x)^2? I don't understand it.

    Thanks
    Offline

    18
    ReputationRep:
    (Original post by vector12)
    Name:  Screenshot_45.png
Views: 15
Size:  20.6 KB
    How does e^2ln(2x) simplify to (2x)^2? I don't understand it.

    Thanks
    Either (a^b)^c = a^{bc} so e^{2\ln(2x)} = \left(e^{\ln(2x)}\right)^2

    or notice that 2\ln(2x) = \ln([2x]^2) using log laws.
    Online

    12
    ReputationRep:
    Well, 2ln(2x) is equivalent to ln(2x)^2 (one of the log rules) and since ln is the inverse of e^x, e^lnx can cancel out to x.
    Online

    20
    ReputationRep:
    (Original post by vector12)
    Name:  Screenshot_45.png
Views: 15
Size:  20.6 KB
    How does e^2ln(2x) simplify to (2x)^2? I don't understand it.

    Thanks
    2Ln(2x) = Ln[(2x)^2]. I assume you know understand that e^Ln(a) = a.
    • Thread Starter
    Offline

    10
    ReputationRep:
    (Original post by _gcx)
    Either (a^b)^c = a^{bc} so e^{2\ln(2x)} = \left(e^{\ln(2x)}\right)^2

    or notice that 2\ln(2x) = \ln([2x]^2) using log laws.
    Wouldn't it be this instead? I thought the power moves up only to be the power of the power, rather than the power of the whole thing.
    (a^b)^c = a^{bc} so e^{2\ln(2x)} = \left(e^{\ln(2x)^2}\right)
    Offline

    18
    ReputationRep:
    (Original post by vector12)
    Wouldn't it be this instead? I thought the power moves up only to be the power of the power, rather than the power of the whole thing.
    (a^b)^c = a^{bc} so e^{2\ln(2x)} = \left(e^{\ln(2x)^2}\right)
    No, (a^b)^c \not\equiv a^{b^c}
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: November 5, 2017
Poll
Do you agree with the proposed ban on plastic straws and cotton buds?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.