Solve the inequality: log_{0.5} (x - 1) > log_{0.5} 4.

Model Answer & Options

Source: Extra Practice

x > 5

1 < x < 5

x < 5

x > 1

Explanation

When the base of a logarithm is between 0 and 1 (decreasing function), removing the logs reverses the inequality sign. So, log_{0.5} (x - 1) > log_{0.5} 4 implies x - 1 < 4, or x 0, so x > 1. Combining these gives 1 < x < 5. Option A incorrectly keeps the inequality direction.

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