What is expand ln(3/(x^4y)) ?

The solution to expand ln(3/(x^4y)) is ln(3)-4ln(x)-ln(y)

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expand ln(3/(x^4y))

expand

ln (\frac{3}{x ^{4} y})

ln (3) - 4 ln (x) - ln (y)

Solution steps

ln (\frac{3}{x ^{4} y})

Apply log rule:

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

ln (\frac{3}{x ^{4} y}) = ln (3) - ln (x^{4} y)

= ln (3) - ln (x^{4} y)

Apply log rule:

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

ln (x^{4} y) = ln (x^{4}) + ln (y)

= ln (3) - (ln (x^{4}) + ln (y))

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (x^{4}) = 4 ln (x)

= ln (3) - (4 ln (x) + ln (y))

- (4 ln (x) + ln (y)) : - 4 ln (x) - ln (y)

= ln (3) - 4 ln (x) - ln (y)

lo g_{7} (52)

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

ln (\frac{4 x}{x + 1})

4.7 + lo g_{10} (\frac{0.2}{0.1})

3 ln ∣ x - 3 ∣ + 5 ln ∣ x + 2 ∣ + \frac{5}{9} ln ∣ 2 x + 3 ∣

What is expand ln(3/(x^4y)) ?
The solution to expand ln(3/(x^4y)) is ln(3)-4ln(x)-ln(y)