Question

Solve the following logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expression. Give the exact answer.​ Then, use a calculator to obtain a decimal​ approximation, correct to two decimal​ places, for the solution.
ln x equals 10
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Part 1
Solve the equation. What is the exact​ solution? Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
The solution set is StartSet nothing EndSet .
  

​(Type an exact answer in terms of e​.)
B.
There are infinitely many solutions.
C.
There is no solution.

Answer 1

To solve the equation \( \ln x = 10 \), we can rewrite it in exponential form:

\[
x = e^{10}
\]

This is the exact solution.

### Part 1: Choose the correct option

The exact solution in terms of \( e \) is:

\[
x = e^{10}
\]

So, the correct choice is:

A. The solution set is \(\{ e^{10} \}\).

### Part 2: Decimal approximation

Now, let's calculate the decimal approximation of \( e^{10} \). Using a calculator, we find:

\[
e^{10} \approx 22026.47
\]

Thus, the solution is approximately \( 22026.47 \) when rounded to two decimal places.

The final answers are:
- Exact solution: \( e^{10} \)
- Decimal approximation: \( 22026.47 \)