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Solve for x, rounding to the nearest hundredth. e^(x)=4 Answer:

Solve for x x , rounding to the nearest hundredth.\newlineex=4 e^{x}=4 \newlineAnswer:

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Full solution

Q. Solve for x x , rounding to the nearest hundredth.\newlineex=4 e^{x}=4 \newlineAnswer:
  1. Write Equation: Write down the equation that needs to be solved.\newlineWe have the equation ex=4e^{x} = 4.
  2. Apply Natural Logarithm: Apply the natural logarithm (ln⁡\ln) to both sides of the equation to solve for xx.\newlineTaking the natural logarithm of both sides, we get ln⁡(ex)=ln⁡(4)\ln(e^{x}) = \ln(4).
  3. Simplify Left Side: Simplify the left side of the equation using the property that ln⁡(ex)=x\ln(e^{x}) = x. This simplifies to x=ln⁡(4)x = \ln(4).
  4. Calculate ln⁡(4)\ln(4): Calculate the value of ln⁡(4)\ln(4) using a calculator.\newlineUsing a calculator, we find that ln⁡(4)≈1.386294361\ln(4) \approx 1.386294361.
  5. Round to Nearest Hundredth: Round the result to the nearest hundredth.\newlineRounding 1.3862943611.386294361 to the nearest hundredth gives us x≈1.39x \approx 1.39.

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