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

The solution to (dx)/x (dx)-1/y (1-ln(x)-ln(y)) is (dx^2)/x-(1-ln(xy))/y

Popular >

simplify (dx)/x (dx)-1/y (1-ln(x)-ln(y))

simplify

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

\frac{d x ^{2}}{x} - \frac{1 - ln ( x y )}{y}

Solution steps

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

Rewrite

- ln (x) - ln (y)

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

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

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln (x) + ln (y) = ln (x y)

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

\frac{d x}{x} d x = \frac{d x ^{2}}{x}

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

= \frac{d x ^{2}}{x} - \frac{- ln ( x y ) + 1}{y}

ln (\frac{2 ^{5}}{3 ^{7}})

\frac{1}{2 π} [\frac{1}{4} ln (\frac{3}{2}) + ln (\frac{4}{3})]

ln (22.08553 - 2) + 3 ln (8.905 - 1)

ln (\frac{4 k + 1}{4 k - 1})

ln (90) - ln (80)

What is (dx)/x (dx)-1/y (1-ln(x)-ln(y)) ?
The solution to (dx)/x (dx)-1/y (1-ln(x)-ln(y)) is (dx^2)/x-(1-ln(xy))/y