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]

**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.

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