Question

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

Answer 1

Correct Answer - 5
` a=(log_(5)175)/(log_(5)245) = (2+log_(5)7)/(1+2 log_(5)7)`
` or a+ 2a log_(5) 7 = 2 + log_(5) 7`
` or log_(5) 7 = (a-2)/(1-2a) ` ...(i)
Now ` b = (log_(5)875)/(log_(5)1715) = (3+log_(5)7)/(1+3log_(5)7)`
` or b+3b log_(5) 7 = 3 + log_(5) 7`
` or log_(5) 7 = (b-3)/(1-3b) ` ...(ii)
From Eqs. (i) and (ii), we get
`(a-2)/(1-2a) = (b-3)/(1-3b)`
` rArr (1-ab)/(a-b) = 5`