Question
Graph the following logarithmic functions. Which has a graph that increases from left to right?(1 point) Responses y=log3x y is equal to the log base 3 of x y=log13x y is equal to the log base 1 third of x y=log−3x y is equal to the log base negative 3 of x y=log25x
Answers
GPT-4o mini
To determine which of the given logarithmic functions has a graph that increases from left to right, let's analyze each function.
1. **\( y = \log_3 x \)**: This is a logarithm with base 3. Logs with a base greater than 1 (like 3) are increasing functions. So, this graph increases from left to right.
2. **\( y = \log_{\frac{1}{3}} x \)**: This is a logarithm with a base less than 1. Logs with a base between 0 and 1 are decreasing functions. Hence, this graph decreases from left to right.
3. **\( y = \log_{-3} x \)**: Logarithms with a negative base are not defined for real numbers in the way we typically use logarithms, so this function does not have a valid graph in the real number system.
4. **\( y = \log_{25} x \)**: This is a logarithm with base 25, which is greater than 1. Like \( \log_3 x \), this function is increasing from left to right.
Based on this analysis, both \( y = \log_3 x \) and \( y = \log_{25} x \) have graphs that increase from left to right.
However, since the question asks which "has a graph that increases from left to right" and typically expects a single answer, the best choice would be:
**Answer: \( y = \log_3 x \)** (as it's the first option given).
1. **\( y = \log_3 x \)**: This is a logarithm with base 3. Logs with a base greater than 1 (like 3) are increasing functions. So, this graph increases from left to right.
2. **\( y = \log_{\frac{1}{3}} x \)**: This is a logarithm with a base less than 1. Logs with a base between 0 and 1 are decreasing functions. Hence, this graph decreases from left to right.
3. **\( y = \log_{-3} x \)**: Logarithms with a negative base are not defined for real numbers in the way we typically use logarithms, so this function does not have a valid graph in the real number system.
4. **\( y = \log_{25} x \)**: This is a logarithm with base 25, which is greater than 1. Like \( \log_3 x \), this function is increasing from left to right.
Based on this analysis, both \( y = \log_3 x \) and \( y = \log_{25} x \) have graphs that increase from left to right.
However, since the question asks which "has a graph that increases from left to right" and typically expects a single answer, the best choice would be:
**Answer: \( y = \log_3 x \)** (as it's the first option given).