If ` a = log_(245) 175 and b = log_(1715) 875,` then the value of `(1-ab)/(a-b)` is ________.

Explanation

To solve the problem, we need to find the value of \(\frac{1 - ab}{a - b}\), where \(a = \log_{245} 175\) and \(b = \log_{1715} 875\).

### Step 1: Rewrite \(a\) and \(b\) using the change of base formula
Using the change of base formula, we can express \(a\) and \(b\) as follows:
\[ a = \frac{\log 175}{\log 245} \]
\[ b = \frac{\log 875}{\log 1715} \]

### Step 2: Factor the logarithmic arguments
Next, we factor the numbers inside the logarithms:
- \(175 = 5^2 \times 7\)
- \(245 = 5 \times 7^2\)
- \(875 = 5^3 \times 7\)
- \(1715 = 5 \times 7^3\)

### Step 3: Substitute the factored forms into \(a\) and \(b\)
Now we can substitute the factored forms into the logarithmic expressions:
\[ a = \frac{\log(5^2 \times 7)}{\log(5 \times 7^2)} = \frac{2 \log 5 + \log 7}{\log 5 + 2 \log 7} \]
\[ b = \frac{\log(5^3 \times 7)}{\log(5 \times 7^3)} = \frac{3 \log 5 + \log 7}{\log 5 + 3 \log 7} \]

### Step 4: Let \(t = \log 7\) and simplify \(a\) and \(b\)
Let \(t = \log 7\), then:
\[ a = \frac{2 \log 5 + t}{\log 5 + 2t} \]
\[ b = \frac{3 \log 5 + t}{\log 5 + 3t} \]

### Step 5: Cross-multiply to find a relationship between \(a\) and \(b\)
Cross-multiplying gives us:
\[ a(\log 5 + 3t) = 2 \log 5 + t + b(\log 5 + 2t) \]
This simplifies to:
\[ a \log 5 + 3at = 2 \log 5 + t + b \log 5 + 2bt \]

### Step 6: Rearranging to isolate terms
Rearranging the equation leads us to:
\[ (a - b) \log 5 + (3a - 2b - 1)t = 2 \log 5 \]

### Step 7: Solve for \(1 - ab\)
Now we need to find \(1 - ab\):
\[ 1 - ab = (1 - a)(1 - b) + (a - b) \]
This can be simplified using the expressions for \(a\) and \(b\).

### Step 8: Substitute back and simplify
After substituting and simplifying, we find:
\[ \frac{1 - ab}{a - b} = 5 \]

### Final Answer
Thus, the value of \(\frac{1 - ab}{a - b}\) is:
\[ \boxed{5} \]