Final answer:
To solve ln x = 5, we recognize that ln is the inverse function of the exponential function with base e. Therefore, e raised to the power of 5 equals x, which is approximately 148.41.
Step-by-step explanation:
To solve the logarithmic equation ln x = 5, we need to understand that the function ln (natural logarithm) is the inverse of the exponential function with base e (where e ≈ 2.71828). So, if ln x = 5, it means that e raised to the power of 5 equals x. To calculate this, we would typically use a calculator.
Performing this calculation on a calculator would provide us with the value for x. Since no base is given for the logarithm, it is understood to be the natural logarithm (logarithm base e). Therefore, e5 = x. Using a calculator, we find that e5 is approximately 148.41, assuming that the standard rules of significant digits apply.
To round to the nearest hundredth, we look at the third decimal place. Since it is less than 5, we do not need to round up. Thus, the answer is approximately 148.41, which corresponds with option b.