Question

which is the best estimate of the value of ln 16?
1.20
2.77
3.23
4.00

Explanation:

Step1: Recall the property of natural logarithm

We know that \(y = \ln x\) is the inverse function of \(y = e^{x}\). We also know that \(e^{3}\approx20.086\) and \(e^{2}\approx7.389\), \(e^{2.77}\approx16\)

Step2: Calculate using the formula

Since \(y=\ln x\) and \(x = e^{y}\). If \(x = 16\), we check the values:

• For \(y = 1.20\), \(e^{1.20}\approx3.32\)
• For \(y = 2.77\), \(e^{2.77}\approx16\)
• For \(y = 3.23\), \(e^{3.23}\approx25.39\)
• For \(y = 4.00\), \(e^{4}\approx54.598\)

Answer:

2.77