Question

Graph the following logarithmic functions. Which has a graph that decreases from left to right?(1 point)
Responses

log2x
log
2
⁡
𝑥
logarithm subscript 2 baseline x

lnx
ln
⁡
𝑥
l n x

log−2x
log
−
2
⁡
𝑥
logarithm subscript negative 2 baseline x

log0.5x

Answer 1

To analyze the behavior of the given logarithmic functions, we need to recognize their properties:

1. **\( \log_2 x \)**: This function is defined for \( x > 0 \) and increases from left to right. It passes through the point \( (1, 0) \) and will be positive for \( x > 1 \) and negative for \( 0 < x < 1 \).

2. **\( \ln x \)**: This is the natural logarithm function, defined for \( x > 0 \). It also increases from left to right, similar to \( \log_2 x \).

3. **\( \log_{-2} x \)**: This function is problematic because a logarithm with a negative base is not defined in the realm of real numbers.

4. **\( \log_{0.5} x \)**: This logarithm has a base of \( 0.5 \) (which is less than 1). Logarithmic functions with bases between 0 and 1 decrease from left to right. Therefore, as \( x \) increases, \( \log_{0.5} x \) will decrease.

### Conclusion:

Among the given functions, **\( \log_{0.5} x \)** has a graph that decreases from left to right.