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logarithm equations

'O' levels & Sec 3 Math & Chemistry Holiday Programmes 2010 (Revision & Headstart)

UPDATE: Early Bird registration is extended to 6 Dec 09, 2359 hours (Singapore time)

Credit: Art Institute of Portland

Most Secondary two students would have received your streaming results, stating the subject combinations for Sec 3 for year 2010, haven't you?
I hope you like the combination as you are going to eat, sleep and breathe those subjects.
For Secondary three students, I hope most if not all of you have been promoted to Sec 4. Pat yourself if you have done well. If you haven't done well, what are you going to do this holiday?
Regardless if you are Sec three or 'O' level students next year, are you ready to rock & roll?

We are excited for 2010!

You don't have to do everything during this holidays, you just need to do 1 - 2 right things while enjoying your break. I'm not even talking about doing your holiday assignments.

  • If your concepts aren't great, build them up by re-learning them!
  • If you aren't practicing enough, start working on sums, doing your five/ten years series!
  • If you hate the subject or have no interest, use this holiday to decide if you are intending to continue or give up, find time sit down and read about the subject, get a friend to explain the annoying concepts to you

“The moment you say 'I know everything' is the end of your growth.”

If you like to experience learning with a difference, spend your holidays more meaningfully, enrich yourself in these 'O' level Math or Chemistry, we would like to extend the invitation to join us at our December Holiday Mastery Workshops & Essential Concepts Revision Programme!

Click here for more details.

O level A-Math: Fatal Mistake In Logarithm Equation You Must Aviod

This is a common mistake I notice in my O level A-Math essential concepts revision workshop.

Solve the following equation:

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First, you must identify the type of question since different types of question require different strategies.
It's a different log-log question.
Strategy required: Change base.

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Change base formula used.
Reason for changing to base 2: Between changing to base 2 or x, we choose base 2 as x is an unknown, we choose not to work with THE unknown most of the time, don't we?

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Since we observe that there is a common term (log2 x),
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image Did you observe the fatal mistake (It's #7 Common mistake in Logarithm?

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The correct way to do the substitution would be:
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Solve the quadratic equation for y. Substitute the value back to find x.

Remember to check for validity of answers.

How To Solve "Clones" Type Of Logarithm Equations

In the previous post, I shared with you on the main Types of Logarithm Equations and How To Identify Them Easily.

Today, I'm going to share with you the step by step approach to solve Clone! type of Logarithm Equations.

Photo by Chris Gin

Clone Dolly

The strategy involving

  • identifying the clone which is relatively easy since clones are items which look EXACTLY the same.
  • Let the clone by y (Substitution method)

[pmath](log_5 x)^2 = 2log_5 x [/pmath]

[pmath] Let log_5 x be y [/pmath]

Substitution:

[pmath]y^2 = 2y [/pmath]

Common Mistake! (Canceling y from each side of the equation; So What? : you will miss out 1 answer)

[pmath]y = 2 [/pmath]

Correct Approach (Shift everything to left hand side so that right hand side is 0; So What? :Ready for factorization since it is a quadratic equation)

[pmath]y^2 - 2y = 0 [/pmath]

[pmath]y(y - 2) = 0 [/pmath]

[pmath]y = 0  or y - 2 = 0 [/pmath]

Remember we are interested in the unknown in the question (x) NOT y!

[pmath]log_5 x = 0  or log_5 x = 2 [/pmath]

[pmath]x = 1  or x = 25 [/pmath]

Check validity of answers by substituting values of x into the original given equation. Both values are acceptable.

Revisit: A-Math Logarithms Equations (Plus: Types of Equations & How To Identify Them Easily)

With the school holidays period at this moment, it is perhaps a good time to revisit some of the 'killer' topics in O Level Math. I will start off with revisiting A-Math Logarithm Equations (Why: Logarithm is a brand new concepts taught only in Sec 3 unlike some other topics which are taught fundamentally in lower Sec; being such a new concept, some students could be a little overwhelmed by what Logarithm is all about)

Previous posts include Solving Reader's Logarithm Equations, Top 7 Commonly Made Mistakes in Logarithms

Photo By zebtron

To solve logarithm equations, it is very important to be able to identify the main types of equations.

Types of Logarithm Equations

There are 4 main types which I have classified:

  1. Only Log (singing to the tune of "Only you" lalalalala.....)
  2. Same Log-Log
  3. Different Log-Log
  4. Clones!

Features of each type of Log Equations

  1. Only Log: Log appears once
  2. Log with same bases (bases are the subscript beside Log)
  3. Log with different bases
  4. Exact looking log appears more than once

Examples for each type as stated above:

  1. [pmath]log_2 \{3x+1}/{2x-7} = 3[/pmath]
  2. [pmath]log_3 (2x+1) - log_3 (x-7) = 2[/pmath]
  3. [pmath]log_4 3y - 2log_2 x = 1[/pmath]
  4. [pmath](log_5 x)^2 = 2log_5 x [/pmath]

In the next post, I will be showing step by step way to solve Clones! type of Logarithm Equations. Ensure you subscribe to our feed to be posted of updates.