What is 1/200 ln(x)-ln(200-x) ?

The solution to 1/200 ln(x)-ln(200-x) is ln((x^{1/200})/(200-x))

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simplify 1/200 ln(x)-ln(200-x)

simplify

\frac{1}{200} ln (x) - ln (200 - x)

ln (\frac{x ^{\frac{1}{200}}}{200 - x})

Solution steps

\frac{1}{200} ln (x) - ln (200 - x)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{1}{200} ln (x) = ln (x^{\frac{1}{200}})

= ln (x^{\frac{1}{200}}) - ln (- x + 200)

Apply log rule:

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

ln (x^{\frac{1}{200}}) - ln (200 - x) = ln (\frac{x ^{\frac{1}{200}}}{- x + 200})

= ln (\frac{x ^{\frac{1}{200}}}{200 - x})

5 ln (a) + 2 ln (b) - 7 ln (c) + 3 ln (2)

4 lo g_{6} (x) + 8 lo g_{6} (y)

ln (x^{2} + 12 x + 11) - ln (x + 1)

lo g_{3} (\frac{9}{x + 6})

- \frac{ln ( \frac{9}{2} )}{3 ln ( 10 )}

What is 1/200 ln(x)-ln(200-x) ?
The solution to 1/200 ln(x)-ln(200-x) is ln((x^{1/200})/(200-x))