To determine which of the given logarithmic functions has a graph that decreases from left to right, let's analyze each function:
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\( \log_2 x \): This is the logarithm base 2. The graph of this function increases from left to right.
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\( \ln x \): This is the natural logarithm (base \( e \)). The graph also increases from left to right.
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\( \log_{0.5} x \): The base of this logarithm (0.5) is less than 1. Logarithmic functions with bases less than 1 decrease from left to right.
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\( \log_{-2} x \): Logarithms with negative bases are not defined for real numbers, so this function does not have a graph in the real number system.
Conclusion:
The function that has a graph that decreases from left to right is \( \log_{0.5} x \).
1 answer