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Consider the equation 4*e^(2.7 x)=33". " Solve the equation for x. Express the solution as a logarithm in base e. x= Approximate the value of x. Round your answer to the nearest thousandth. x~~

Consider the equation\newline4⋅e2.7x=33.  4 \cdot e^{2.7 x}=33 \text {. } \newlineSolve the equation for x x . Express the solution as a logarithm in basee e .\newlinex= x= \newlineApproximate the value of x x . Round your answer to the nearest thousandth.\newlinex≈ x \approx

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Q. Consider the equation\newline4⋅e2.7x=33.  4 \cdot e^{2.7 x}=33 \text {. } \newlineSolve the equation for x x . Express the solution as a logarithm in basee e .\newlinex= x= \newlineApproximate the value of x x . Round your answer to the nearest thousandth.\newlinex≈ x \approx
  1. Isolate exponential term: Isolate the exponential term e2.7xe^{2.7x} by dividing both sides of the equation by 44.\newlineCalculation: 4⋅e2.7x=33⇒e2.7x=3344\cdot e^{2.7x} = 33 \Rightarrow e^{2.7x} = \frac{33}{4}
  2. Take natural logarithm: Take the natural logarithm (log base ee, denoted as ln⁡\ln) of both sides to solve for xx.\newlineCalculation: ln⁡(e2.7x)=ln⁡(334)\ln(e^{2.7x}) = \ln(\frac{33}{4})
  3. Apply logarithm property: Apply the property of logarithms that ln⁡(ey)=y\ln(e^y) = y to simplify the left side of the equation.\newlineCalculation: 2.7x=ln⁡(334)2.7x = \ln(\frac{33}{4})
  4. Solve for x: Solve for x by dividing both sides of the equation by 2.72.7.\newlineCalculation: x=ln⁡(334)2.7x = \frac{\ln(\frac{33}{4})}{2.7}
  5. Approximate x value: Approximate the value of x using a calculator.\newlineCalculation: x≈ln⁡(334)/2.7≈ln⁡(8.25)/2.7≈2.1102/2.7≈0.781x \approx \ln(\frac{33}{4}) / 2.7 \approx \ln(8.25) / 2.7 \approx 2.1102 / 2.7 \approx 0.781

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