What is log_{e}(2x-5)-log_{e}(1-(2x-5)) ?

The solution to log_{e}(2x-5)-log_{e}(1-(2x-5)) is ln((2x-5)/(-2x+6))

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simplify log_{e}(2x-5)-log_{e}(1-(2x-5))

simplify

lo g_{e} (2 x - 5) - lo g_{e} (1 - (2 x - 5))

ln (\frac{2 x - 5}{- 2 x + 6})

Solution steps

lo g_{e} (2 x - 5) - lo g_{e} (1 - (2 x - 5))

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

lo g_{e} (2 x - 5) - lo g_{e} (1 - (2 x - 5)) = lo g_{e} (\frac{2 x - 5}{- ( 2 x - 5 ) + 1})

= lo g_{e} (\frac{2 x - 5}{1 - ( 2 x - 5 )})

Expand

1 - (2 x - 5) : - 2 x + 6

= lo g_{e} (\frac{2 x - 5}{- 2 x + 6})

Apply log rule:

lo g_{e} (x) = ln (x)

= ln (\frac{2 x - 5}{- 2 x + 6})

25000 lo g_{2} (1 + 1010)

ln (\frac{x}{e ^{t}})

lo g_{7} (3 x^{4})

ln (sin^{2} (x) cos (x))

ln (x) + ln (3) + ln (6)

What is log_{e}(2x-5)-log_{e}(1-(2x-5)) ?
The solution to log_{e}(2x-5)-log_{e}(1-(2x-5)) is ln((2x-5)/(-2x+6))