Question

match each equation with a graph above 10^{x} a. blue (b) log(x) b. black (k) e^{x} c. green (g) ln(x) d. red (r)

Explanation:

Step1: Analyze the growth rate of exponential functions

The function \(y = 10^{x}\) has a very fast - growing rate compared to \(y=e^{x}\) (since \(10>e\approx2.718\)). The blue curve (B) has a steeper growth among the exponential - like curves.

Step2: Analyze the logarithmic functions

The function \(y = \log(x)=\frac{\ln(x)}{\ln(10)}\) grows more slowly than \(y=\ln(x)\) (because \(\ln(10)> 1\), so for \(x > 1\), \(\ln(x)>\log(x)\)). The green curve (G) grows more slowly than the red curve (R).

Answer:

\(10^{x}\) - a. blue (B); \(\log(x)\) - c. green (G); \(e^{x}\) - b. black (K); \(\ln(x)\) - d. red (R)