Common Algebra Mistakes
Example: Solving a Logarithm Equation

The Goal

Solve the following equation for x (where a and b are (positive) constants):


The Mistake

Find the algebra mistake:


(Roll the mouse over the algebra to see a hint in red)

The Correction


(Roll the mouse over the area above to see the correction in blue)

An Explanation

There are two mistakes. The first is a careless error; a must be subtracted from both sides to isolate the a·ln(bx) term. The second mistake apparently was to assume that ln(1) = 1 and hence bx = 1. But ln(1) = 0. The correct way to proceed is to use the equivalence


which we can also view as an action by saying we take e to the expression on each side, and since y=ex and y=ln(x) are inverse functions of each other, the left side simplifies to the inside of the natural logarithm expression.

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