What is (-(y/x)^2)/2+8/7 y/x-3/7 ln(y/x) ?

The solution to (-(y/x)^2)/2+8/7 y/x-3/7 ln(y/x) is -(y^2)/(2x^2)+(8y)/(7x)-3/7 (ln(y)-ln(x))

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simplify (-(y/x)^2)/2+8/7 y/x-3/7 ln(y/x)

simplify

\frac{- ( \frac{y}{x} ) ^{2}}{2} + \frac{8}{7} \frac{y}{x} - \frac{3}{7} ln (\frac{y}{x})

- \frac{y ^{2}}{2 x ^{2}} + \frac{8 y}{7 x} - \frac{3}{7} (ln (y) - ln (x))

Solution steps

\frac{- ( \frac{y}{x} ) ^{2}}{2} + \frac{8}{7} \cdot \frac{y}{x} - \frac{3}{7} 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{- ( \frac{y}{x} ) ^{2}}{2} + \frac{8}{7} \cdot \frac{y}{x} - \frac{3}{7} (ln (y) - ln (x))

\frac{- ( \frac{y}{x} ) ^{2}}{2} = - \frac{y ^{2}}{2 x ^{2}}

= - \frac{y ^{2}}{2 x ^{2}} + \frac{8}{7} \cdot \frac{y}{x} - \frac{3}{7} (ln (y) - ln (x))

Multiply

\frac{8}{7} \cdot \frac{y}{x} : \frac{8 y}{7 x}

= - \frac{y ^{2}}{2 x ^{2}} + \frac{8 y}{7 x} - \frac{3}{7} (ln (y) - ln (x))

8.07428 ln \frac{P}{( P - 90 )} - 8.07428 ln (\frac{4}{41})

- lo g_{10} (3.98 \cdot 1 0^{- 7})

3.14 + lo g_{10} (\frac{1.875}{0.625})

e ln (ey) - e - ln (y) + 1

ln (\frac{24}{74})

What is (-(y/x)^2)/2+8/7 y/x-3/7 ln(y/x) ?
The solution to (-(y/x)^2)/2+8/7 y/x-3/7 ln(y/x) is -(y^2)/(2x^2)+(8y)/(7x)-3/7 (ln(y)-ln(x))