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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

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)

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

lo g_{5} (5 x)

ln (\frac{1 - \infty}{1 + \infty})

\frac{1}{4} ln (\frac{3}{7})

ln (\frac{1 + a}{b})

lo g_{10} (x^{2} - 1) 1 + lo g_{10} (x - 1)

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