SOLUTION: Explain the error in the "proof" that 2 is less than 1.
1. 1/9 is less than 1/3
2. 1/3 squared is less than 1/3
3. log 1/3 is less than log 1/3
4. 2log 1/3 is les
Question 31874: Explain the error in the "proof" that 2 is less than 1.
1. 1/9 is less than 1/3
2. 1/3 squared is less than 1/3
3. log 1/3 is less than log 1/3
4. 2log 1/3 is less than 1log 1/3
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Notice that log(1/3) is a negative number. The last step before concluding that 2 < 1 was:
Now, you divide both side by log(1/3). However, since it's a negative number, you also have to 'flip' the inequality (whenever you multiply or divide an inequality by a negative number, you must flip the inequality). SO the actual result would be:
which is correct.
Here's an example of why you must flip it. Suppose you have . Now multiply both sides by -1. If you don't flip the inequality, you would get which is obviously wrong.
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