Questions: Solve the following exponential equation. Round your answer to three decimal places. 50(e^0.94 x)=85 x=

Solution Steps

To solve the exponential equation \(50(e^{0.94x}) = 85\), we first isolate the exponential term by dividing both sides by 50. Then, we take the natural logarithm of both sides to solve for \(x\). Finally, we divide by the coefficient of \(x\) in the exponent to find the value of \(x\).

Starting with the equation: \[ 50(e^{0.94x}) = 85 \] we divide both sides by 50 to isolate the exponential term: \[ e^{0.94x} = \frac{85}{50} = 1.7 \]

Next, we take the natural logarithm of both sides: \[ \ln(e^{0.94x}) = \ln(1.7) \] Using the property of logarithms, this simplifies to: \[ 0.94x = \ln(1.7) \]

Now, we solve for \(x\) by dividing both sides by 0.94: \[ x = \frac{\ln(1.7)}{0.94} \approx 0.5645 \] Rounding to three decimal places, we have: \[ x \approx 0.564 \]

Final Answer