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We start with the following inequality:
(1/81)>(1/243)
That is:
(1/3)4>(1/3)5
Applying the decimal logarithm on both sides we get:
log10(1/3)4> log10(1/3)5
Applying the power property of the logarithms we have:
4 log10(1/3)> 5 log10(1/3)
Splitting both sides by log10(1/3) we came to the conclusion:
4>5
Obviously this demonstration has an error, as we all know that 4 is not greater than 5 (or does anyone have any questions?). Click below to find out what the error is:
In this demonstration comes a stage where we have:
4 log10(1/3)> 5 log10(1/3)
According to the demonstration, the next step would be:
Split both sides by log10(1/3)
There is the mistake !!!
Because log10(1/3) it's a negative number, right?
So we are dividing both sides of the inequality by a NEGATIVE number.
This would cause the relational operator of the equation to invert, which would lead us to the correct conclusion that:
4 < 5
Next: 2 + 2 equals 5?
