What is ln(1/(x/y)) ?

The solution to ln(1/(x/y)) is -(ln(x)-ln(y))

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simplify ln(1/(x/y))

simplify

ln (\frac{1}{\frac{x}{y}})

- (ln (x) - ln (y))

Solution steps

ln (\frac{1}{\frac{x}{y}})

Apply log rule:

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

ln (\frac{1}{\frac{x}{y}}) = ln (1) - ln (\frac{x}{y})

= ln (1) - ln (\frac{x}{y})

Apply log rule:

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

ln (\frac{x}{y}) = ln (x) - ln (y)

= ln (1) - (ln (x) - ln (y))

Apply log rule:

lo g_{a} (1) = 0

= 0 - (ln (x) - ln (y))

0 - (ln (x) - ln (y)) = - (ln (x) - ln (y))

= - (ln (x) - ln (y))

ln (y) + ln (1 - x^{2})

\frac{1}{2 - 4} ln (\frac{2}{4})

5 lo g_{3} (x) + 3 lo g_{3} (y)

ln (\frac{40}{11})

ln (x + y) + ln (x - y) + ln (x^{6})