What is 3ln(xy)-4ln(y)+21n(x^2) ?

The solution to 3ln(xy)-4ln(y)+21n(x^2) is ln((x^3)/y)+21nx^2

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simplify 3ln(xy)-4ln(y)+21n(x^2)

simplify

3 ln (x y) - 4 ln (y) + 21 n (x^{2})

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

Solution steps

3 ln (x y) - 4 ln (y) + 21 n (x^{2})

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}) - 4 ln (y) + 21 n (x^{2})

Apply log rule:

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

4 ln (y) = ln (y^{4})

= ln ((x y)^{3}) - ln (y^{4}) + 21 n (x^{2})

Apply log rule:

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

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

= ln (\frac{( x y ) ^{3}}{y ^{4}}) + 21 n x^{2}

Simplify

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

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

\frac{ln ( v ) - 2 ln ( cos ( v ) )}{2}

60 ln (\frac{5.981}{1.711})

ln (\frac{23.25}{372})

ln (\frac{2.5198}{0.05})

ln (\frac{x - i}{x + i})

What is 3ln(xy)-4ln(y)+21n(x^2) ?
The solution to 3ln(xy)-4ln(y)+21n(x^2) is ln((x^3)/y)+21nx^2