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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply the fraction rule:

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

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

lo g_{10} (\frac{a c}{b})

lo g_{x} ((a) (4))

lo g_{11} (\frac{x}{7})

lo g_{5} (8 x)

ln (5 x^{2})

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