Questions: Solve the logarithmic equation. ln(4x) = 8.7 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 a comma to separate answers as needed.) B. The solution is the empty set.

Solve the logarithmic equation.
ln(4x) = 8.7

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 a comma to separate answers as needed.)
B. The solution is the empty set.

Transcript text: Solve the logarithmic equation. $\ln 4 \mathrm{x}=8.7$ Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is $\square$ \}. (Type an exact answer in simplified form. Use a comma to separate answers as needed.) B. The solution is the empty set.

Solution

Solution Steps

To solve the logarithmic equation $\ln 4x = 8.7$, we need to isolate $x$. We can do this by exponentiating both sides of the equation to eliminate the natural logarithm. This involves using the property that if $\ln a = b$, then $a = e^b$. After isolating $x$, we can compute its value using Python.

Step 1: Isolate the Variable

We start with the equation: \[ \ln(4x) = 8.7 \] To eliminate the natural logarithm, we exponentiate both sides: \[ 4x = e^{8.7} \]

Step 2: Solve for $x$

Next, we isolate $x$ by dividing both sides by 4: \[ x = \frac{e^{8.7}}{4} \]

Step 3: Calculate the Value

Calculating $e^{8.7}$ gives approximately $1500.7281$. Thus, we find: \[ x \approx \frac{1500.7281}{4} \approx 375.1820 \]