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A logarithm is a mathematical function that represents the power to which a base number must be raised to produce a given number. It is expressed as log_{b}(x) where b is the base and x is the number.
An inequality is a mathematical statement that compares two quantities or expressions and states that one is greater than, less than, or not equal to the other.
When dividing an inequality by a negative value, you need to flip the inequality sign. For example, if the inequality is x < 5 and you divide both sides by -2, the new inequality would be x > -2. This is because when you divide by a negative value, you are essentially multiplying by a negative value, which flips the direction of the inequality.
Dividing an inequality by a negative value can be tricky because it can change the direction of the inequality. This is why it is important to always remember to flip the inequality sign when dividing by a negative value.
A logarithm inequality includes a logarithm function on one or both sides of the inequality. This means that the solutions may not be the same as a regular inequality and may need to be checked for validity. It is important to remember the properties of logarithms, such as log_{b}(x) = y is equivalent to b^{y} = x, when solving logarithm inequalities.