What is 3ln(x^2y)-21ln(xy)+1 ?

The solution to 3ln(x^2y)-21ln(xy)+1 is -ln(x^{15}y^{18})+1

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simplify 3ln(x^2y)-21ln(xy)+1

simplify

3 ln (x^{2} y) - 21 ln (x y) + 1

- ln (x^{15} y^{18}) + 1

Solution steps

3 ln (x^{2} y) - 21 ln (x y) + 1

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}) - 21 ln (x y) + 1

Apply log rule:

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

21 ln (x y) = ln ((x y)^{21})

= ln ((x^{2} y)^{3}) - ln ((x y)^{21}) + 1

Apply log rule:

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

ln ((x^{2} y)^{3}) - ln ((x y)^{21}) = ln (\frac{( x ^{2} y ) ^{3}}{( x y ) ^{21}})

= ln (\frac{( x ^{2} y ) ^{3}}{( x y ) ^{21}}) + 1

Simplify

\frac{( x ^{2} y ) ^{3}}{( x y ) ^{21}} : \frac{1}{x ^{15} y ^{18}}

= ln (\frac{1}{x ^{15} y ^{18}}) + 1

ln (\frac{1}{x ^{15} y ^{18}}) = - ln (x^{15} y^{18})

= - ln (x^{15} y^{18}) + 1

- lo g_{10} (4.8 \cdot 1 0^{- 4})

lo g_{2} (2^{5})

ln (\frac{s}{5 p})

ln ((x^{2} + 1) (x - 1))

ln (a (a + 1)^{5})

What is 3ln(x^2y)-21ln(xy)+1 ?
The solution to 3ln(x^2y)-21ln(xy)+1 is -ln(x^{15}y^{18})+1