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Approaching logarithm problems


Andy K.

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Hi all,

So, I'm preparing for a unit test tomorrow on exponents and logarithms, and I am noticing a trend myself.

Especially for some complex log/ln equations, I have a great difficulty knowing where and how to go about solving a problem. 

When I take a look at the answer key, it all makes sense, even the process. It's just that when I attempt solving them on my own, I tend to get stuck at some point. 

I have a good knowledge on log laws as well as exponent ones however, they do not come to my mind whenever their use is required in a proble (if you know what I mean)

I know it takes a ton of practice to feel natural (Which I am doing rn), but I'm looking for advice as to how to go about solving any equations involving log/ln.

Here is an example I am stuck with:

Solve for x:

ln (x)= 4log(base)x(e)

*Just on a side note, a quick advice on exponential equations/word problem questions would be wonderful!

Thank you for reading and all your help. I really need them at this point!

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For your specific problem, a hint: try expressing everything in terms of ln (change of base formula).  

As for your main question, practice definitely helps, as you point out.  In terms of what I do, I usually attempt to express everything in terms of one single base, and then just experiment around with simplifying everything using the log laws as appropriate.  Sometimes, you may find that it helps to 'reverse' the log laws.  For example, you may rewrite logc(a) + logc(b) = logc(ab), or b*logc(a) = logc(ab).  Overall though, the main thing to do is to just practice, especially using difficult log and exponential equations, and don't give up on the problems, even if you really just want to look at the answers.  I've found that I learn best if I just keep going until I finally get the answer independently.  

For exponential equations, the only thing I can really say is to become familiar using a combination of both log and exponential notation.  Sometimes one is more convenient than the other, depending on the situation.  

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59 minutes ago, Andy K. said:

When I take a look at the answer key, it all makes sense, even the process. It's just that when I attempt solving them on my own, I tend to get stuck at some point. 

I have a good knowledge on log laws as well as exponent ones however, they do not come to my mind whenever their use is required in a proble (if you know what I mean)

I know it takes a ton of practice to feel natural (Which I am doing rn), but I'm looking for advice as to how to go about solving any equations involving log/ln.

Luckily in HL exams most (at least Part A) questions are repeats of types of problems that appeared on previous exams. You will likely encounter similar struggles in later units. In light of which, it's really hard for us to summarize every possible problem solving approach. In your homework (or if you have time), just try all the different formula you know. Assume you don't know the steps and you look at your equations, log (ab) and log(a/b) are useless right now (for first step). So essentially you would either try to raise to some power or change of base. Attempt 1: Raise everything to the power of e. x = e^(4 logx e). Attempt 2: Raise everything to power of x. x^ (ln x) =e^4. Attempt 3: change of base to ln: ln x = 4ln e / ln x. This seems most promising. Now you don't have time to do trial and error for every question on the actual exam, but this offers a back up plan in case you see a new question type.

If you have the time, I would not recommend looking at the manual for a step-by-step solution. In homework just first time go through do all the problems you can do. Then you go back and use different strategies to tackle questions you stumbled the first time. If you are aiming for a 6 or 7, it's worth to sometimes spend 30-60 minutes on a single question, where upon knowing the right strategy, the same question would only take minutes on the exam. Practicing problems is not for just getting the answers, it's also very good practice in choosing strategies to approach questions. 

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  • 3 months later...
On 2017-2-15 at 11:31 AM, Andy K. said:

Hi all,

So, I'm preparing for a unit test tomorrow on exponents and logarithms, and I am noticing a trend myself.

Especially for some complex log/ln equations, I have a great difficulty knowing where and how to go about solving a problem. 

When I take a look at the answer key, it all makes sense, even the process. It's just that when I attempt solving them on my own, I tend to get stuck at some point. 

I have a good knowledge on log laws as well as exponent ones however, they do not come to my mind whenever their use is required in a proble (if you know what I mean)

I know it takes a ton of practice to feel natural (Which I am doing rn), but I'm looking for advice as to how to go about solving any equations involving log/ln.

Here is an example I am stuck with:

Solve for x:

ln (x)= 4log(base)x(e)

*Just on a side note, a quick advice on exponential equations/word problem questions would be wonderful!

Thank you for reading and all your help. I really need them at this point!

Hi, how did you go in that unit test of logarithm and exponents. Were the questions familiar to you, or where there many unfamiliar or hard to gras? Your answer will be much appreciated as I am also preparing for exponents and logarithm Hl maths. I am really worried.

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