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Nov/08

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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)

(log_5 x)^2 = 2log_5 x

Let log_5 x be y

Substitution:

y^2 = 2y

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

y = 2

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)

y^2 - 2y = 0

y(y - 2) = 0

y = 0  or y - 2 = 0

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

log_5 x = 0  or log_5 x = 2

x = 1  or x = 25

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

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1 Comment for How To Solve “Clones” Type Of Logarithm Equations

singaporeolevelmaths | GCE O Level A-Math E-Math Chemistry Coaching, Tuition, Tutor, Class, Revision, Notes, Tips, Concepts, Questions | February 23, 2009 at 1:18 pm

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About Ai Ling

Hi, my name is Ai Ling Ong and I'm a professional Math Trainer specializing in GCE 'O' level Mathematics (Additional & Elementary). More than 10 years of teaching experience, I have coached hundreds of students more than 80 schools in Singapore. Read more about me here
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