Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    0
    ReputationRep:
    Ok I get logs , but there is just one rule i dont get:

    How does a^\log_a x = X ?

    I get that if you log the LHS to get  \log_a a^(log_a x)

    then take the top log down and it becomes a sum of the 2 logs. Then  \log_a a =1 so i'm left with just  \log_a x but how does that = x?
    • Community Assistant
    • Study Helper
    Offline

    20
    ReputationRep:
    Community Assistant
    Study Helper
    You've forgotton to 'unlog' once you logged the LHS:

    \displaystyle \log_a a^{log_a x} = \log_a x \log_a a = \log_a x

    Now if log_a b_1 = log_a b_2 then b_1=b_2. Use this to prove the result.
    • Thread Starter
    Offline

    0
    ReputationRep:
    Ooooo ok So im just doing a^loga x again but the a^ and the log cancel?

    Just like log and 10^ will cancel?
    • Wiki Support Team
    Offline

    14
    ReputationRep:
    Wiki Support Team
    (Original post by Carlo08)
    Ooooo ok So im just doing a^loga x again but the a^ and the log cancel?

    Just like log and 10^ will cancel?
    Yes, exactly that. In fact, if you believe that, then go and read your original question again and it becomes obvious that a^{\log_a x} = x.
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Brexit voters: Do you stand by your vote?
    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
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • 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.