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The key takeaway from the tutorial is the application of the one-to-one property in solving the equation 5^x-3+2=8. The first step is to isolate the exponent by subtracting 2 from both sides. This results in 5^x-3=6. Since we cannot directly apply the one-to-one property, taking the log base 5 of both sides allows us to simplify the equation to x-3=log base 5 of 6.