What is simplify-3ln(x)+x+xy+y-3ln(y) ?

The solution to simplify-3ln(x)+x+xy+y-3ln(y) is -ln(x^3y^3)+x+xy+y

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simplify-3ln(x)+x+xy+y-3ln(y)

simplify

- 3 ln (x) + x + x y + y - 3 ln (y)

- ln (x^{3} y^{3}) + x + x y + y

Solution steps

- 3 ln (x) + x + x y + y - 3 ln (y)

Apply log rule:

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

3 ln (x) = ln (x^{3})

= - ln (x^{3}) + x + x y + y - 3 ln (y)

Apply log rule:

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

3 ln (y) = ln (y^{3})

= - ln (x^{3}) + x + x y + y - ln (y^{3})

Rewrite

- ln (x^{3}) - ln (y^{3})

- (ln (x^{3}) + ln (y^{3}))

= - (ln (x^{3}) + ln (y^{3})) + x + x y + y

Apply log rule:

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

ln (x^{3}) + ln (y^{3}) = ln (x^{3} y^{3})

= - ln (x^{3} y^{3}) + x + x y + y

2 lo g_{10} (2 + 3)

- lo g_{10} (3.8 \cdot 1 0^{- 5})

ln (\frac{3 x ^{5}}{y})

ln (8 c)

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

What is simplify-3ln(x)+x+xy+y-3ln(y) ?
The solution to simplify-3ln(x)+x+xy+y-3ln(y) is -ln(x^3y^3)+x+xy+y