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?