We are given four graphs (green, black, red, blue) and four equations (10x10^x10x, exe^xex, log(x)\log(x)log(x), ln(x)\ln(x)ln(x)). We need to match the graphs with the corresponding equations.
The equations 10x10^x10x and exe^xex represent exponential functions. Their graphs are increasing curves that pass through the point (0,1). Since e≈2.718<10e \approx 2.718 < 10e≈2.718<10, the graph of exe^xex grows slower than 10x10^x10x. Looking at the provided image, the blue (B) curve is steeper than the green (G) curve. Therefore, the blue (B) graph represents 10x10^x10x, and the green (G) graph represents exe^xex.
The equations log(x)\log(x)log(x) and ln(x)\ln(x)ln(x) represent logarithmic functions. Their graphs are increasing curves that pass through the point (1,0). Since log(x)\log(x)log(x) is the logarithm base 10 and ln(x)\ln(x)ln(x) is the logarithm base eee, and e<10e < 10e<10, the graph of ln(x)\ln(x)ln(x) grows faster than log(x)\log(x)log(x). Looking at the provided image, the black (K) curve is steeper than the red (R) curve. Therefore, the black (K) graph represents ln(x)\ln(x)ln(x), and the red (R) graph represents log(x)\log(x)log(x).
10x10^x10x: d. blue (B) exe^xex: a. green (G) log(x)\log(x)log(x): c. red (R) ln(x)\ln(x)ln(x): b. black (K) \\( \boxed{ \begin{aligned} 10^x &: \text{ d. blue (B)} \\ e^x &: \text{ a. green (G)} \\ \log(x) &: \text{ c. red (R)} \\ \ln(x) &: \text{ b. black (K)} \end{aligned} } \\)
Oops, Image-based questions are not yet availableUse Solvely.ai for full features.
Failed. You've reached the daily limit for free usage.Please come back tomorrow or visit Solvely.ai for additional homework help.