A logarithmic function of the form \( y=a+b \log (x-4) \) passes through the points \( (5,17) \) and \( (879,-38) \). Find \( a \) and \( b \), rounding all values to three decimal places, if necessary. Answer Attempt 1 out of 2 \( a=\square b=\square \)

To find the constants \( a \) and \( b \) in the equation \( y = a + b \log(x - 4) \) that passes through the points \( (5, 17) \) and \( (879, -38) \), we'll substitute these points into the equation to create a system of equations. 1. For the point \( (5, 17) \): \[ 17 = a + b \log(5 - 4) \implies 17 = a + b \log(1) \implies 17 = a + 0 \implies a = 17 \] 2. For the point \( (879, -38) \): \[ -38 = 17 + b \log(879 - 4) \implies -38 = 17 + b \log(875) \] Rearranging this gives: \[ -38 - 17 = b \log(875) \implies -55 = b \log(875) \] Now we can solve for \( b \): \[ b = \frac{-55}{\log(875)} \] Using a calculator, \( \log(875) \approx 2.943 \), thus: \[ b \approx \frac{-55}{2.943} \approx -18.67 \] Now rounding gives: \[ a = 17, \quad b \approx -18.667 \] Finally, rounding \( b \) to three decimal places gives: \[ a = 17, \quad b = -18.667 \] So, the values are: \( a = 17, \quad b = -18.667 \)