What is 3x^2(12ln(x)-2ln(3))+12x^2 ?

The solution to 3x^2(12ln(x)-2ln(3))+12x^2 is 3x^2ln((x^{12})/9)+12x^2

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simplify 3x^2(12ln(x)-2ln(3))+12x^2

simplify

3 x^{2} (12 ln (x) - 2 ln (3)) + 12 x^{2}

3 x^{2} ln (\frac{x ^{12}}{9}) + 12 x^{2}

Solution steps

3 x^{2} (12 ln (x) - 2 ln (3)) + 12 x^{2}

Apply log rule:

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

12 ln (x) = ln (x^{12})

= 3 x^{2} (ln (x^{12}) - 2 ln (3)) + 12 x^{2}

Apply log rule:

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

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

= 3 x^{2} (ln (x^{12}) - ln (3^{2})) + 12 x^{2}

Apply log rule:

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

ln (x^{12}) - ln (3^{2}) = ln (\frac{x ^{12}}{3 ^{2}})

= 3 x^{2} ln (\frac{x ^{12}}{3 ^{2}}) + 12 x^{2}

3^{2} = 9

= 3 x^{2} ln (\frac{x ^{12}}{9}) + 12 x^{2}

ln (\frac{37.4}{22.1})

lo g_{e} (\frac{x ^{3 x}}{3 ^{3 x}})

5.96 - 5 lo g_{10} (\frac{3.5}{10})

lo g_{b} (w) + 6 lo g_{b} (v)

ln (\frac{( x + 4 )}{x - 1})

What is 3x^2(12ln(x)-2ln(3))+12x^2 ?
The solution to 3x^2(12ln(x)-2ln(3))+12x^2 is 3x^2ln((x^{12})/9)+12x^2