What is 3ln(x)-4ln(x+3)+ln(y) ?

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

- 8000 \cdot ln (\frac{400}{1000})

ln (x^{a - 1} (1 - x)^{b - 1})

ln (v x^{5})

2000 ln (\frac{140000}{140000 - 2100 x}) - 9.8 x

2 ln (x) + ln (x + 2)

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