Part 3 of 3
Solve the following logarithmic equation. Be sure to reject any value of 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. 0 of 2

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
(Type an exact answer. Type your answer using exponential notation.)
B. There are infinitely many solutions.
C. There is no solution.
What is the decimal approximation to the solution? Select the correct choice below and, if necessary, fill in
the answer box to complete your choice.
A. The solution set is . .
(yype an integer or decimal rounded to two decimal places as needed.)
B. There are infinitely many solutions.
C. There is no solution.

Ask by Ford Pena. in the United States

Mar 31,2025

Question

Part 3 of 3
Solve the following logarithmic equation. Be sure to reject any value of 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. 0 of 2

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
(Type an exact answer. Type your answer using exponential notation.)
B. There are infinitely many solutions.
C. There is no solution.
What is the decimal approximation to the solution? Select the correct choice below and, if necessary, fill in
the answer box to complete your choice.
A. The solution set is . .
(yype an integer or decimal rounded to two decimal places as needed.)
B. There are infinitely many solutions.
C. There is no solution.

Ask by Ford Pena. in the United States

Mar 31,2025

UpStudy AI · Accepted Answer

We start with the logarithmic equation: $$ 6 + 8 \ln x = 5 $$.
Subtract 6 from both sides to isolate the logarithmic term: 
$$ 8 \ln x = 5 - 6 $$
This simplifies to:
$$ 8 \ln x = -1 $$
Next, divide both sides by 8:
$$ \ln x = -\frac{1}{8} $$
To solve for $$ x $$, exponentiate both sides:
$$ x = e^{-\frac{1}{8}} $$
Since the logarithm is defined for $$ x > 0 $$, and $$ e^{-\frac{1}{8}} $$ is positive, this value is in the domain.Exact SolutionThe exact solution is $$ x = e^{-\frac{1}{8}} $$. Thus, the correct choice is A: The solution set is $$ \left\{ e^{-\frac{1}{8}} \right\} $$.
The exact solution is $$ x = e^{-\frac{1}{8}} $$. The decimal approximation is approximately 0.88.

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