Questions: Match each equation with a graph above: 10^x a. green (G) e^x b. black (K) log (x) c. red (R) ln (x) d. blue (B)

Match each equation with a graph above:
10^x
a. green (G)
e^x
b. black (K)
log (x)
c. red (R)
ln (x)
d. blue (B)
Transcript text: Match each equation with a graph above: $10^{x}$ a. green (G) $e^{x}$ b. black (K) $\log (x)$ c. red (R) $\ln (x)$ d. blue (B)
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Solution

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Solution Steps

Step 1: Analyze the graphs and equations

We are given four graphs (green, black, red, blue) and four equations (10x10^x, exe^x, log(x)\log(x), ln(x)\ln(x)). We need to match the graphs with the corresponding equations.

Step 2: Exponential functions

The equations 10x10^x and exe^x represent exponential functions. Their graphs are increasing curves that pass through the point (0,1). Since e2.718<10e \approx 2.718 < 10, the graph of exe^x grows slower than 10x10^x. Looking at the provided image, the blue (B) curve is steeper than the green (G) curve. Therefore, the blue (B) graph represents 10x10^x, and the green (G) graph represents exe^x.

Step 3: Logarithmic functions

The equations log(x)\log(x) and ln(x)\ln(x) represent logarithmic functions. Their graphs are increasing curves that pass through the point (1,0). Since log(x)\log(x) is the logarithm base 10 and ln(x)\ln(x) is the logarithm base ee, and e<10e < 10, the graph of ln(x)\ln(x) grows faster than 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), and the red (R) graph represents log(x)\log(x).

Final Answer

10x10^x: d. blue (B) exe^x: a. green (G) log(x)\log(x): c. red (R) 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} } \\)

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