What is ln(3)+2ln(x)-9ln(y) ?

The solution to ln(3)+2ln(x)-9ln(y) is ln((3x^2)/(y^9))

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simplify ln(3)+2ln(x)-9ln(y)

simplify

ln (3) + 2 ln (x) - 9 ln (y)

ln (\frac{3 x ^{2}}{y ^{9}})

Solution steps

ln (3) + 2 ln (x) - 9 ln (y)

Apply log rule:

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

2 ln (x) = ln (x^{2})

= ln (3) + ln (x^{2}) - 9 ln (y)

Apply log rule:

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

ln (3) + ln (x^{2}) = ln (3 x^{2})

= ln (3 x^{2}) - 9 ln (y)

Apply log rule:

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

9 ln (y) = ln (y^{9})

= ln (3 x^{2}) - ln (y^{9})

Apply log rule:

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

ln (3 x^{2}) - ln (y^{9}) = ln (\frac{3 x ^{2}}{y ^{9}})

= ln (\frac{3 x ^{2}}{y ^{9}})

ln (\frac{r}{s})

ln (x) + 2 ln (y + 1) - \frac{1}{2} ln (z)

3 ln ∣ 5 ∣ - 3 ln ∣ 2 ∣

ln (2 u)

lo g_{7} (\frac{9 x ^{2}}{y ^{3}})

What is ln(3)+2ln(x)-9ln(y) ?
The solution to ln(3)+2ln(x)-9ln(y) is ln((3x^2)/(y^9))