What is ((ln| y/x+4|-6ln|(y/x-1)|))/5 ?

The solution to ((ln| y/x+4|-6ln|(y/x-1)|))/5 is (ln((x^6|y+4x|)/(|x|(y-x)^6)))/5

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simplify ((ln| y/x+4|-6ln|(y/x-1)|))/5

simplify

\frac{( ln \frac{y}{x} + 4 - 6 ln ( \frac{y}{x} - 1 ) )}{5}

\frac{ln ( \frac{x ^{6} ∣ y + 4 x ∣}{∣ x ∣ ( y - x ) ^{6}} )}{5}

Solution steps

\frac{( ln \frac{y}{x} + 4 - 6 ln ( \frac{y}{x} - 1 ) )}{5}

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

6 ln (\frac{y}{x} - 1) = ln ((\frac{y}{x} - 1)^{6})

= \frac{( ln \frac{y}{x} + 4 - ln ( ( \frac{y}{x} - 1 ) ^{6} ) )}{5}

Apply log rule:

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

ln \frac{y}{x} + 4 - ln ((\frac{y}{x} - 1)^{6}) = ln (\frac{\frac{y}{x} + 4}{\frac{y}{x} - 1 ^{6}})

= \frac{ln ( \frac{∣ \frac{y}{x} + 4 ∣}{∣ \frac{y}{x} - 1 ∣ ^{6}} )}{5}

Simplify

\frac{\frac{y}{x} + 4}{( \frac{y}{x} - 1 ) ^{6}} : \frac{x ^{6} ∣ y + 4 x ∣}{∣ x ∣ ( y - x ) ^{6}}

= \frac{ln ( \frac{x ^{6} ∣ y + 4 x ∣}{∣ x ∣ ( y - x ) ^{6}} )}{5}

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

\frac{1}{4} x^{2} (2 ln^{2} (3 x) - 2 ln (3 x) + 1)

ln (2 + x) - ln (2)

ln (\frac{6.35 \cdot 1 0 ^{- 3}}{0.00555})

ln (\frac{e ^{4}}{19})

What is ((ln| y/x+4|-6ln|(y/x-1)|))/5 ?
The solution to ((ln| y/x+4|-6ln|(y/x-1)|))/5 is (ln((x^6|y+4x|)/(|x|(y-x)^6)))/5