Question
Graph the following logarithmic functions. Which has a graph that increases from left to right?(1 point)
Responses
y=log3 x
y is equal to the log base 3 of x
y=log1/3 x
y is equal to the log base 1 third of x
y=log−3/x
y is equal to the log base negative 3 of x
y=log2/5 x
Responses
y=log3 x
y is equal to the log base 3 of x
y=log1/3 x
y is equal to the log base 1 third of x
y=log−3/x
y is equal to the log base negative 3 of x
y=log2/5 x
Answers
GPT-4o mini
To determine which of the given logarithmic functions has a graph that increases from left to right, we need to analyze the bases of the logarithms for each function.
1. **\(y = \log_3 x\)**: This is a logarithm with base \(3\), which is greater than \(1\). The graph of this function increases as \(x\) increases.
2. **\(y = \log_{\frac{1}{3}} x\)**: This is a logarithm with base \(\frac{1}{3}\), which is between \(0\) and \(1\). The graph of this function decreases as \(x\) increases.
3. **\(y = \log_{-3} x\)**: Logarithms with a negative base are not defined for real numbers, so this function does not exist in a real context.
4. **\(y = \log_{\frac{2}{5}} x\)**: This is a logarithm with a base less than \(1\) (specifically, \(\frac{2}{5}\)). The graph of this function also decreases as \(x\) increases.
From this analysis, the only function that has a graph that increases from left to right is **\(y = \log_3 x\)**.
1. **\(y = \log_3 x\)**: This is a logarithm with base \(3\), which is greater than \(1\). The graph of this function increases as \(x\) increases.
2. **\(y = \log_{\frac{1}{3}} x\)**: This is a logarithm with base \(\frac{1}{3}\), which is between \(0\) and \(1\). The graph of this function decreases as \(x\) increases.
3. **\(y = \log_{-3} x\)**: Logarithms with a negative base are not defined for real numbers, so this function does not exist in a real context.
4. **\(y = \log_{\frac{2}{5}} x\)**: This is a logarithm with a base less than \(1\) (specifically, \(\frac{2}{5}\)). The graph of this function also decreases as \(x\) increases.
From this analysis, the only function that has a graph that increases from left to right is **\(y = \log_3 x\)**.