What is 2(ln((x-25)/(25)+1)-ln((x-25)/(25)-1)) ?

The solution to 2(ln((x-25)/(25)+1)-ln((x-25)/(25)-1)) is 2ln(x/(x-50))

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simplify 2(ln((x-25)/(25)+1)-ln((x-25)/(25)-1))

simplify

2 (ln (\frac{x - 25}{25} + 1) - ln (\frac{x - 25}{25} - 1))

2 ln (\frac{x}{x - 50})

Solution steps

2 (ln (\frac{x - 25}{25} + 1) - ln (\frac{x - 25}{25} - 1))

Apply log rule:

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

ln (\frac{x - 25}{25} + 1) - ln (\frac{x - 25}{25} - 1) = ln (\frac{\frac{x - 25}{25} + 1}{\frac{x - 25}{25} - 1})

= 2 ln (\frac{\frac{x - 25}{25} + 1}{\frac{x - 25}{25} - 1})

Simplify

\frac{\frac{x - 25}{25} + 1}{\frac{x - 25}{25} - 1} : \frac{x}{x - 50}

= 2 ln (\frac{x}{x - 50})

ln (40) - ln (400)

ln (\frac{x - 1}{x}) + c

2 + 3 lo g_{10} (x) - \frac{1}{2} lo g_{10} (x + 7)

lo g_{a} (\frac{y ^{5} w ^{2}}{x ^{4} z ^{3}})

ln (\frac{1}{( r - 1 ) !} θ^{- r} x^{(r - 1)} e^{(- x θ - 1)})

What is 2(ln((x-25)/(25)+1)-ln((x-25)/(25)-1)) ?
The solution to 2(ln((x-25)/(25)+1)-ln((x-25)/(25)-1)) is 2ln(x/(x-50))