A logarithmic function of the form \( y=a+b \log (x-4) \) passes through the points \( (5,2) \) and \( (190,-24) \). Find \( a \) and \( b \), rounding all values to three decimal places, if necessary. Answer Attempt 2 out of 2 \( a=\square=\square \)

To find \( a \) and \( b \), you can substitute the \( x \) and \( y \) values from the points into the equation \( y=a+b\log(x-4) \). For the point \( (5,2) \): \[ 2 = a + b \log(5-4) \] \[ 2 = a + b \log(1) \] Since \(\log(1) = 0\), this simplifies to: \[ a = 2 \] For the point \( (190,-24) \): \[ -24 = a + b \log(190-4) \] Subtracting \( 2 \) from both sides gives: \[ -24 - 2 = b \log(186) \] \[ -26 = b \log(186) \] Now, calculate \( \log(186) \): \[ \log(186) \approx 2.270 \] Thus: \[ -26 = b \times 2.270 \] Solving for \( b \): \[ b \approx \frac{-26}{2.270} \approx -11.436 \] So, rounding to three decimal places: \( a = 2.000 \) \( b \approx -11.436 \) Therefore, \( a = 2.000 \) \( b = -11.436 \)