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Chapter 16: Problem 2

If \(\ln (x)=3.2\), what is \(x\) ? a) \(18.65\) b) \(24.53\) c) \(31.83\) d) \(64.58\)

Short Answer

Expert verified
a) 10.12 b) 24.53 c) 32.13 d) 7.85 Answer: b) 24.53

Step by step solution

01

Understand the natural logarithm function

The natural logarithm of a number x is denoted as \(\ln(x)\). It is the inverse function of exponentiation with base e (Euler's number, approximately equal to 2.718). In other words, if we have a logarithm equation \(\ln(x) = y\), we can rewrite it as an exponentiation equation: \(e^y = x\).
02

Use the given information in the equation

We are given the equation \(\ln(x) = 3.2\). To find the value of x, we need to rewrite the equation as an exponentiation equation with e as the base: \(e^{3.2} = x\)
03

Calculate the value of x

Now we can calculate the value of x by finding \(e^{3.2}\). Using a calculator or an online tool, we find that \(e^{3.2} \approx 24.53\)
04

Match the calculated value with the given options

We calculated the value of x as approximately 24.53. Matching this with the given options, we find that \(x \approx 24.53\), which corresponds to option b. So, the correct answer is option b) \(24.53\).

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