Hey there! Sign in to join this conversationNew here? Join for free

A-level Maths - ln(x) - Natural Logs... HELP? watch

    Offline

    19
    ReputationRep:
    (Original post by Philip-flop)
    x
    When dealing with e, use ln.

    It's the same as going log to the base e. The reason this is so useful is lne = 1, making life much easier.
    Offline

    10
    ReputationRep:
    (Original post by Philip-flop)
    Oh yay. At least I kind of got the question right. But how do I give my answer in terms of \ln 2 ??
    express 8 as a power of 2 and go from there
    Offline

    10
    ReputationRep:
    (Original post by Philip-flop)
    Oh yay. At least I kind of got the question right. But how do I give my answer in terms of \ln 2 ??
    Watch this whole video https://www.youtube.com/watch?v=imKALH7eAZ4

    then you'll find these questions more than doable...
    Offline

    10
    ReputationRep:
    (Original post by Philip-flop)
    Oh yay. At least I kind of got the question right. But how do I give my answer in terms of \ln 2 ??
    Is there a power relationship between 2 and 8 you can exploit?
    Remembering that log(x^a)=alog(x)?
    • Thread Starter
    Offline

    18
    ReputationRep:
    Ok guys. With your help I think I managed to finally get the answer. As seen below...
    Name:  Photo 03-09-2016, 11 12 48.jpg
Views: 40
Size:  134.0 KB

    (Original post by Jasaron)
    When dealing with e, use ln.

    It's the same as going log to the base e. The reason this is so useful is lne = 1, making life much easier.
    Thank you. I decided to take your advice and replace log(e) with ln(e). Your help was very useful!

    (Original post by ValerieKR)
    Is there a power relationship between 2 and 8 you can exploit?
    Remembering that log(x^a)=alog(x)?
    Thanks for your help!! I didn't even think of replacing the 8 with a 2^3!! How did you know to do that?

    (Original post by Naruke)
    Watch this whole video https://www.youtube.com/watch?v=imKALH7eAZ4

    then you'll find these questions more than doable...
    I only watched half of that video before some things started making more sense! Thank you so much!! Going to watch the rest of the video today
    • Community Assistant
    • Welcome Squad
    Online

    20
    ReputationRep:
    Community Assistant
    Welcome Squad
    (Original post by Philip-flop)
    Thank you. I decided to take your advice and replace log(e) with ln(e). Your help was very useful!

    Nope nope nope. You can't do that. log(e) and ln(e) are two completely different things, you cannot just switch between the two because they're not equal. log(e) is dealing with base 10 while ln(e) deals with base e which is why it goes away (as it's equal to 1). That would only be valid if you rewrote ln(e) as log_e(e)
    • Thread Starter
    Offline

    18
    ReputationRep:
    (Original post by RDKGames)
    Nope nope nope. You can't do that. log(e) and ln(e) are two completely different things, you cannot just switch between the two because they're not equal. log(e) is dealing with base 10 while ln(e) deals with base e which is why it goes away (as it's equal to 1). That would only be valid if you rewrote ln(e) as log_e(e)
    OMG. Oops I'm so stupid for having done that! I wrote the 4th line out completely wrong as it is
    • Thread Starter
    Offline

    18
    ReputationRep:
    Ok. So I've scrapped my last answer and decided to start again. This time without taking logs to both sides! I'm probably still wrong though haha Sorry if I'm frustrating any of you guys

    Attachment 577582577584
    Attached Images
      
    Online

    22
    ReputationRep:
    (Original post by RDKGames)
    Nope nope nope. You can't do that. log(e) and ln(e) are two completely different things, you cannot just switch between the two because they're not equal. log(e) is dealing with base 10 while ln(e) deals with base e which is why it goes away (as it's equal to 1). That would only be valid if you rewrote ln(e) as log_e(e)
    btw \log = \ln for almost every mathematician. \log = \log_{10} for engineers.
    Online

    22
    ReputationRep:
    (Original post by Philip-flop)
    Ok. So I've scrapped my last answer and decided to start again. This time without taking logs to both sides! I'm probably still wrong though haha

    Yeah, that's correct
    Offline

    10
    ReputationRep:
    (Original post by Philip-flop)
    Thanks for your help!! I didn't even think of replacing the 8 with a 2^3!! How did you know to do that?
    Reducing log(a^x) to xlog(a) is a standard move with logs ^.^

    I use the word logs to mean a logarithm with any base - in maths you'll take ln 99% of the time and in engineering 'log' will normally mean log base 10
    • Thread Starter
    Offline

    18
    ReputationRep:
    (Original post by Zacken)
    Yeah, that's correct
    Yayyyy. I finally got it. Still a bit confused but at least I'm getting there, right?!
    Shame I don't know how to work this question out when I take logs to both sides
    • Community Assistant
    • Welcome Squad
    Online

    20
    ReputationRep:
    Community Assistant
    Welcome Squad
    (Original post by Philip-flop)
    Yayyyy. I finally got it. Still a bit confused but at least I'm getting there, right?!
    Shame I don't know how to work this question out when I take logs to both sides
    Your method still involves taking logs of both sides, it's just that those logs are the special case of logs called "natural logarithms" in this case. When you say take logs, that would mean the same thing regardless of the base.
    Online

    22
    ReputationRep:
    (Original post by Philip-flop)
    Yayyyy. I finally got it. Still a bit confused but at least I'm getting there, right?!
    Shame I don't know how to work this question out when I take logs to both sides
    You did take logs to both sides, just without knowing it. When moving from your first to your second line, you did it.

    From: e^{3x} = 8, you take \log_e to both sides to get \log_e e^{3x} = \log_e 8.

    Using the power rule gets you 3x \log_e e = \log_e 8.

    But you know that \log_a a = 1 so \log_e e = 1 specifically.

    So your equation becomes 3x = \log_e 8 as you've written down. You did take logs to both sides, just without knowing it.
    • Thread Starter
    Offline

    18
    ReputationRep:
    (Original post by Zacken)
    You did take logs to both sides, just without knowing it. When moving from your first to your second line, you did it.

    From: e^{3x} = 8, you take \log_e to both sides to get \log_e e^{3x} = \log_e 8.

    Using the power rule gets you 3x \log_e e = \log_e 8.

    But you know that \log_a a = 1 so \log_e e = 1 specifically.

    So your equation becomes 3x = \log_e 8 as you've written down. You did take logs to both sides, just without knowing it.
    Oh yeah!! Thank you so much for clearing that up for me!! That actually makes perfect sense! You made me realise that I did take logs to both sides its just the LHS was "hidden" in a way.

    (Original post by RDKGames)
    Your method still involves taking logs of both sides, it's just that those logs are the special case of logs called "natural logarithms" in this case. When you say take logs, that would mean the same thing regardless of the base.
    Yes I'm still trying to get used to the fact that... \log_e (x) is the same as \ln (x)
    Online

    22
    ReputationRep:
    (Original post by Philip-flop)
    Oh yeah!! Thank you so much for clearing that up for me!! That actually makes perfect sense! You made me realise that I did take logs to both sides its just the LHS was "hidden" in a way.
    No worries.
 
 
 
Poll
Do you agree with the PM's proposal to cut tuition fees for some courses?
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.