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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.

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.