Question

question 22
match each equation with a graph above
10^x
e^x
ln(x)
log(x)
a. red (r)
b. blue (b)
c. green (g)
d. black (k)

Explanation:

Step1: Analyze the growth rate of exponential functions

The function \(y = 10^{x}\) grows faster than \(y=e^{x}\) for \(x>0\) since \(10>e\approx2.718\). So \(y = 10^{x}\) corresponds to the steeper - growing exponential curve.

Step2: Analyze the logarithmic functions

The function \(y=\ln(x)\) has a larger slope than \(y = \log(x)\) (where \(\log(x)\) is the common logarithm, base - 10). The domain of \(y=\ln(x)\) and \(y=\log(x)\) is \(x>0\).

Answer:

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