MHB Logarithm inequality divide an inequality by a negative value

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The discussion centers on the error in handling logarithmic inequalities when dividing by a negative value. Specifically, it highlights that since \(\log_{10}\left(\frac{1}{2}\right)<0\), dividing the inequality by a negative number necessitates reversing the inequality direction. This leads to the conclusion that the correct interpretation results in \(2<3\). Understanding this principle is crucial for accurately solving logarithmic inequalities. Properly applying this rule prevents misinterpretation of results in mathematical expressions.
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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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