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.
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.
Solution
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.