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If \( \ln (4 x+2)=1 \), then \( x=\square \)

Ask by Paul Johnson. in the United States
Jan 22,2025

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\( x = \frac{e - 2}{4} \)

Solución

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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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 \( \frac{e - 2}{4} \).

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