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
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]
[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.