# 4 is greater than 5?

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Let's check:

(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?