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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

lo g_{10} (11.1 + 3) + lo g_{10} (11.1 - 4)

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

ln (\frac{7 - 1 ^{2}}{1 + 1})

- ln (∣ x + 4 ∣^{15} ∣ 3 x + 2 ∣) - \frac{68}{x + 4}

\frac{( 6 ln ( x ) + 16 - 6 ln ( 4 ) )}{x}

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