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Explanation:

Step1: Recall properties of logarithmic functions

The function $y = \ln(x)$ and $y=\log(x)$ (assuming base - 10 for $\log(x)$) are logarithmic functions. The domain of $y = \ln(x)$ and $y=\log(x)$ is $x>0$. The graph of $y = \ln(x)$ and $y=\log(x)$ increases slowly for $x>1$. The graph of $y = \ln(x)$ has a steeper slope than $y=\log(x)$ for $x > 1$. The graph of $y=\log(x)$ is the blue graph (B) and the graph of $y=\ln(x)$ is the black graph (K).

Step2: Recall properties of exponential functions

The functions $y = 10^{x}$ and $y = e^{x}$ are exponential functions. The function $y = e^{x}\approx2.718^{x}$ and $y = 10^{x}$. For exponential functions $y = a^{x}$ with $a>1$, they are increasing functions. The function $y = 10^{x}$ grows faster than $y = e^{x}$ for positive $x$. The graph of $y = 10^{x}$ is the red graph (R) and the graph of $y = e^{x}$ is the green graph (G).

Answer:

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