Question
Solve the logarithmic equation Be sure to reject any value of x that is not in the domain of the original logarithmic expression. 3ln(4x)=9 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 in simplified form. Use integers or fractions for any numbers in the expression.) B. There are infinitely many solutions. C. There is no solution.
Answer
4.7
(326 Votes)
Sophie
Veteran · Tutor for 11 years
Answer
To solve the logarithmic equation \(3 \ln (4x) = 9\), follow these steps:1. Divide both sides by 3 to isolate the natural logarithm:
2. Exponentiate both sides to remove the natural logarithm, using the fact that \(e^{\ln(a)} = a\):
3. Divide both sides by 4 to solve for
:
4. Check the domain: The original logarithmic expression requires
, so
. Since
, the solution
is valid.The exact solution is
, which means the correct choice is:A. The solution set is
.