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

The solution to 3ln(3)-12ln(x^3+2x) is ln((27)/((x^3+2x)^{12)})

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

simplify

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

ln (\frac{27}{( x ^{3} + 2 x ) ^{12}})

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

3^{3} = 27

= ln (\frac{27}{( x ^{3} + 2 x ) ^{12}})

ln (10 x - 25) - 2 ln (x)

ln (\frac{36000000}{9000000})

ln (\frac{2}{3 ^{2} 5 ^{4}})

ln (92) - ln (32)

0.01 \cdot ln (0.95 \cdot 10000)

What is 3ln(3)-12ln(x^3+2x) ?
The solution to 3ln(3)-12ln(x^3+2x) is ln((27)/((x^3+2x)^{12)})