Let's check:

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:

log_{10}(1/3)^{4}> log_{10}(1/3)^{5}

Applying the power property of the logarithms we have:

4 log_{10}(1/3)> 5 log_{10}(1/3)

Splitting both sides by log_{10}(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 log _{10}(1/3)> 5 log_{10}(1/3)**

According to the demonstration, the next step would be:

Split both sides by **log _{10}(1/3)**

**There is the mistake !!!**

Because **log _{10}(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**