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

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

Popular >

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

simplify

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

ln (y^{3})

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

(x y)^{3} y : x^{3} y^{4}

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

Apply log rule:

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

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

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

Simplify

\frac{x ^{3} y ^{4}}{x ^{3} y} : y^{3}

= ln (y^{3})

\frac{1}{3} ln (x) + \frac{10}{12} (x + 3) - \frac{1}{6} ln (x - 3)

\frac{1}{2} ln (5) - ln (2)

4.74 + lo g_{10} (\frac{0.81245}{0.24745})

ln (1300) - ln (100 \cdot e^{0.09})

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