Logarithm inequality divide an inequality by a negative value

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highmath
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What is error in the picture?
 
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  • Four lines of inequalities: 1/4 > 1/8; (1/2)^2 > (1/2)^3; 2log10(1/2) > 3log10(1/2); 2 > 3.
    logaritmquestion.PNG
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Discussion

The error arises because:

$$\log_{10}\left(\frac{1}{2}\right)<0$$

When we divide an inequality by a negative value, we need to reverse the direction of the inequality, so that we get:

$$2<3$$
 

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