Solve the equation for x. (Enter your answers as a comma-separated list.)
ln(4 − 5x) = 4

To solve the equation \(\ln(4 - 5x) = 4\), follow these steps:

### Step 1: Exponentiate both sides
The equation is:
\[
\ln(4 - 5x) = 4
\]
To remove the natural logarithm, exponentiate both sides using the base \(e\):
\[
4 - 5x = e^4
\]

### Step 2: Solve for \(x\)
Rearrange the equation to solve for \(x\):
\[
-5x = e^4 - 4
\]
\[
x = \frac{4 - e^4}{5}
\]

Thus, the solution is:
\[
x = \frac{4 - e^4}{5}
\]

### Final Answer
\[
x = \frac{4 - e^4}{5}
\]

Would you like further details or explanations on any step?

Here are 5 related questions:
1. How do you solve natural logarithm equations in general?
2. What properties of logarithms are useful in equations like this?
3. How do you verify if a solution is valid in a logarithmic equation?
4. What is the value of \(e^4\) approximately?
5. How do you solve equations involving logarithms with bases other than \(e\)?

**Tip:** Always check if the argument of the logarithm is positive when solving logarithmic equations.

Solve the equation for x. (Enter your answers as a comma-separated list.) ln(4 − 5x) = 4

Learn to solve the natural logarithmic equation ln(4 − 5x) = 4 using exponentiation and algebraic rearrangement. Follow a step-by-step solution, including key logarithmic properties and exponential concepts. This problem is ideal for high school students in Grades 10-12.

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