Solve the inequality log₀.₅ (x - 3) < log₀.₅ 5.

Model Answer & Options

Source: Extra Practice

x < 8

x > 8

3 < x < 8

x > 3

Explanation

When the base of a logarithm is between 0 and 1 (as is 0.5), the inequality sign flips when comparing the arguments. So, log₀.₅ (x - 3) 5. This leads to x > 8. Also, for the logarithm to be defined, x - 3 > 0 (x > 3), which is already satisfied by x > 8. Therefore, the solution is x > 8.

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