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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

2 \cdot ln (3) - 2 \cdot ln (2)

lo g_{4} (\frac{1 2 ^{3}}{7 ^{6}})

- lo g_{10} (3.5 \cdot 1 0^{- 2})

ln (\frac{e ^{2} - e ^{4} - 1}{2 - 5})

\frac{1}{2} ln (20)

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