Question
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Tutor-Verified Answer
Answer
\( x = \frac{e - 2}{4} \)
Solution
To solve the equation:
\[
\ln(4x + 2) = 1
\]
Follow these steps:
1. **Exponentiate both sides** to eliminate the natural logarithm:
\[
4x + 2 = e^1 = e
\]
2. **Isolate \( x \)**:
\[
4x = e - 2
\]
\[
x = \frac{e - 2}{4}
\]
**Final Answer:**
\[
x = \frac{\,e\; -\; 2\,}{\,4\,}
\]
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Simplify this solution Mind Expander
To solve the equation \( \ln (4x + 2) = 1 \), we start by exponentiating both sides to eliminate the natural logarithm. This gives us \( 4x + 2 = e^1 \), which simplifies to \( 4x + 2 = e \). Next, we isolate \( 4x \) by subtracting 2 from both sides: \( 4x = e - 2 \). Finally, we divide by 4 to solve for \( x \): \[ x = \frac{e - 2}{4} \] So the solution for \( x \) is \( \frac{e - 2}{4} \).
