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

The solution to ln(3/(4x^4y)) is ln(3)-2ln(2)-4ln(x)-ln(y)

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

simplify

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

ln (3) - 2 ln (2) - 4 ln (x) - ln (y)

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

ln (4) = 2 ln (2)

= ln (3) - (4 ln (x) + ln (y) + 2 ln (2))

- (2 ln (2) + 4 ln (x) + ln (y)) : - 2 ln (2) - 4 ln (x) - ln (y)

= ln (3) - 2 ln (2) - 4 ln (x) - ln (y)

lo g_{2} (5) + lo g_{2} (x) - lo g_{2} (3)

lo g_{10} (5 t)

8 lo g_{b} (x) + 9 lo g_{b} (z)

lo g_{4} (5) - lo g_{4} (9)

lo g_{2} (x + 1) - lo g_{2} (x - 1)

What is ln(3/(4x^4y)) ?
The solution to ln(3/(4x^4y)) is ln(3)-2ln(2)-4ln(x)-ln(y)