What is 3ln(x^2y)-2ln(y) ?

The solution to 3ln(x^2y)-2ln(y) is ln(x^6y)

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simplify 3ln(x^2y)-2ln(y)

simplify

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

ln (x^{6} y)

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

\frac{( x ^{2} y ) ^{3}}{y ^{2}} : x^{6} y

= ln (x^{6} y)

\frac{d}{d x} (ln (x)) + ln (2 x)

ln (\frac{3.635}{1.29})

ln ((1 + tan (y)) (sin (x) - 1))

ln (\frac{15}{28.6})

(\frac{2}{18}) ln (\frac{2}{18})