Questions: Solve for x . ln x=5 Select the correct choice below and, if necessary, fill in the ans A. The solution is x= . (Type an exact answer in simplified form. Type expone answers as needed.) B. The solution is not a real number.

Solve for x .
ln x=5

Select the correct choice below and, if necessary, fill in the ans
A. The solution is x= .
(Type an exact answer in simplified form. Type expone answers as needed.)
B. The solution is not a real number.
Transcript text: Solve for x . \[ \ln x=5 \] Select the correct choice below and, if necessary, fill in the ans A. The solution is $x=$ $\square$ . (Type an exact answer in simplified form. Type expone answers as needed.) B. The solution is not a real number.
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Solution

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Solution Steps

Step 1: Understand the Problem

We are given the equation \(\ln x = 5\) and need to solve for \(x\). The natural logarithm function, \(\ln\), is the inverse of the exponential function with base \(e\).

Step 2: Apply the Inverse Function

To solve for \(x\), we apply the exponential function to both sides of the equation. This will eliminate the natural logarithm:

\[ e^{\ln x} = e^5 \]

Since \(e^{\ln x} = x\), we have:

\[ x = e^5 \]

Step 3: Choose the Correct Option

The problem provides two options. Since we have found a real number solution for \(x\), we select option A.

Final Answer

The solution is \(\boxed{x = e^5}\).

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