A logarithmic function of the form $$ y=a+b \log (x-1) $$ passes through the points $$ (2,15) $$ and $$ (173,-12) $$. Find $$ a $$ and $$ b $$, rounding all values to three decimal places, if necessary. Answer Ancompt rout of 2 $$ a=\square b=\square $$

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We are given the function
$$
y = a + b \log (x-1)
$$
which passes through the points $$(2,15)$$ and $$(173,-12)$$.

1. For the point $$(2,15)$$, substitute $$x=2$$ and $$y=15$$:
   $$
   15 = a + b \log (2-1) \quad \Rightarrow \quad 15 = a + b \log 1
   $$
   Since $$\log 1 = 0$$, we immediately have:
   $$
   a = 15.
   $$

2. For the point $$(173,-12)$$, substitute $$x=173$$ and $$y=-12$$:
   $$
   -12 = 15 + b \log (173-1) \quad \Rightarrow \quad -12 = 15 + b \log 172.
   $$
   Solve for $$b$$ by isolating the term with $$b$$:
   $$
   -12 - 15 = b \log 172 \quad \Rightarrow \quad -27 = b \log 172.
   $$
   Thus,
   $$
   b = \frac{-27}{\log 172}.
   $$
   
3. Assuming the base of the logarithm is 10, we calculate:
   $$
   \log 172 \approx 2.235.
   $$
   Then,
   $$
   b \approx \frac{-27}{2.235} \approx -12.087.
   $$

Rounded to three decimal places, we have:
$$
a = 15 \quad \text{and} \quad b \approx -12.087.
$$

The answer is:
$$
a=\boxed{15} \quad b=\boxed{-12.087}.
$$
$$ a = 15 $$ and $$ b \approx -12.087 $$.

A logarithmic function of the form \( y=a+b \log (x-1) \) passes through the points \( (2,15) \) and \( (173,-12) \). Find \( a \) and \( b \), rounding all values to three decimal places, if necessary. Answer Ancompt rout of 2 \( a=\square b=\square \)

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