Questions: Solve for x in the equation below. Round your answer to the nearest hundredth. Do not round any intermediate computations. e^(-3x)=9 x=

Solve for x in the equation below. Round your answer to the nearest hundredth. Do not round any intermediate computations. e^(-3x)=9 x=
Transcript text: Solve for $x$ in the equation below. Round your answer to the nearest hundredth. Do not round any intermediate computations. \[ e^{-3 x}=9 \] \[ x= \]
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Solution

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Solution Steps

Step 1: Start with the equation $2.718^{-3x} = 9$.
Step 2: Take the natural logarithm (ln) of both sides to get $ln(2.718^{-3x}) = ln(9)$.
Step 3: Use the property of logarithms to bring the exponent in front: $-3x \cdot ln(2.718) = ln(9)$.
Step 4: Solve for $x$ by isolating it: $x = \frac{ln(9)}{-3 \cdot ln(2.718)} = -0.73$.

Final Answer

$x = -0.73$

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