If `a = log_245 175` and `b = log_1715 875`, then the value of `(1-ab)/(a-b)` is

Explanation

Here,
`a = log_(245)175 = log175/log245 = log(5^2*7)/log(7^2*5) = (2log5+log7)/(2log7+log5)`

`b = log_(1715)875 = log875/log1715 = log(5^3*7)/log(7^3*5) = (3log5+log7)/(3log7+log5)`

Mow, let `log 5 = p and log 7 = q`

Then,

`a = (2p+q)/(2q+p)` and `b = (3p+q)/(3q+p)`

`:. (1-ab)/(a-b) = (1-(2p+q)/(2q+p)*(3p+q)/(3q+p))/((2p+q)/(2q+p)- (3p+q)/(3q+p))`

`=((2q+p)(3q+p)-(2p+q)(3p+q))/((2p+q)(3q+p)-(2q+p)(3p+q))`

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