This is how I originally taught students to solve these kinds of exponential equations, and I think it’s more useful for nasty type problems that they might see in PreCalculus (when x is in both exponents). But this year I found that I got a lot of mileage out of the idea of rewriting the equation in log form (so log (of base 1/3) of (1/2) = x+2). I think there is a lot of good thought going on in their brains when they convert between log form and exponent form, so most students chose the second approach on the assessments.

 

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