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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

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

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

Simplify

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

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

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ln (\frac{a ^{- 2}}{b ^{4} c ^{- 3}})

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