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Create your own example of solving an exponential equation, with work shown, that includes at least one mistake that a student could easily make (for example: a common calculation error, or a forgotten or misordered step).

27 = 3^3 or mistakenly 27 = -3^3

so x = +3

Exponential equation:

3^x = 27

Work:

x = log3(27)

Mistake:

x = log3(27) + 1

Corrected Work:

x = log3(27)

Did you know?

Did you know that when solving exponential equations, it's important to watch out for common mistakes that students can easily make? Let's consider an example: Suppose we have the equation 2^(3x+1) = 8. To solve it, we would want to isolate the exponent on one side. However, a common mistake students make is to forget to take the logarithm of both sides in the correct order. Mistake Example: Let's say a student mistakenly takes the logarithm of only the left side of the equation: log(2^(3x+1)). They erroneously believe that this simplifies to (3x+1)log(2). Then, to solve for x, they divide both sides by (3log2), leading to (3x+1) = 8 / (3log2). Finally, by subtracting 1 and simplifying, the student arrives at the incorrect solution: x = (8 / (3log2)) - 1. The mistake occurred because the student didn't remember to apply the logarithm to both sides of the equation at the same time. Remember, it's crucial to consistently apply the logarithm to both sides of the equation when solving exponential equations, to ensure accurate and successful solutions.