Questions: Solve. 10 e^(5-x)+9=29 If the answer is not an integer, enter it as a decimal rounded to the nearest hundredth, if needed. x=

Solution Steps

To solve the equation \(10 e^{5-x} + 9 = 29\), we first isolate the exponential term by subtracting 9 from both sides. Then, divide by 10 to solve for the exponential expression. Next, take the natural logarithm of both sides to solve for \(x\).

Starting with the equation: \[ 10 e^{5-x} + 9 = 29 \] we subtract 9 from both sides: \[ 10 e^{5-x} = 20 \]

Next, we divide both sides by 10: \[ e^{5-x} = 2 \]

Taking the natural logarithm of both sides gives us: \[ 5 - x = \ln(2) \]

Rearranging the equation to solve for \(x\): \[ x = 5 - \ln(2) \] Calculating the value, we find: \[ x \approx 4.3069 \] Rounding to the nearest hundredth, we have: \[ x \approx 4.31 \]

Final Answer