## 2 < 1Math brain teasers require computations to solve.Sue was disappointed after Bob showed her that 2 was not, in fact, equal to 1. She was not quite done, though. She told Bob that while 2 may not be equal to 1, she could show conclusively that 2 was in fact less than 1. Bob said it couldn't be done, of course, and Sue offered the following:
Proof: 1 < 2 Multiply the equation by log (0.5) 1 * log(0.5) < 2 * log(0.5) Make the log factors exponents log(0.5 ^ 1) < log(0.5 ^ 2) Carry out the exponentiation log(0.5) < log(0.25) Raise 10 to the power of each side of the inequality 10^(log(0.5)) < 10^(log(0.25)) By definition of logarithms, 10^log(a) = a, so... 0.5 < 0.25 Then just multiply both sides by 4 2 < 1 Question: Bob found the problem almost immediately. Can you? ## What Next?
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