What is ln(((3x+4)^3)/(3(x^2-12)^4)) ?

The solution to ln(((3x+4)^3)/(3(x^2-12)^4)) is 3ln(3x+4)-ln(3)-4ln(x^2-12)

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simplify ln(((3x+4)^3)/(3(x^2-12)^4))

simplify

ln (\frac{( 3 x + 4 ) ^{3}}{3 ( x ^{2} - 12 ) ^{4}})

3 ln (3 x + 4) - ln (3) - 4 ln (x^{2} - 12)

Solution steps

ln (\frac{( 3 x + 4 ) ^{3}}{3 ( x ^{2} - 12 ) ^{4}})

Apply log rule:

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

ln (\frac{( 3 x + 4 ) ^{3}}{3 ( x ^{2} - 12 ) ^{4}}) = ln ((3 x + 4)^{3}) - ln (3 (x^{2} - 12)^{4})

= ln ((3 x + 4)^{3}) - ln (3 (x^{2} - 12)^{4})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln ((3 x + 4)^{3}) = 3 ln (3 x + 4)

= 3 ln (3 x + 4) - ln (3 (x^{2} - 12)^{4})

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (3 (x^{2} - 12)^{4}) = ln (3) + ln ((x^{2} - 12)^{4})

= 3 ln (3 x + 4) - (ln ((x^{2} - 12)^{4}) + ln (3))

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln ((x^{2} - 12)^{4}) = 4 ln (x^{2} - 12)

= 3 ln (3 x + 4) - (ln (3) + 4 ln (x^{2} - 12))

- (ln (3) + 4 ln (x^{2} - 12)) : - ln (3) - 4 ln (x^{2} - 12)

= 3 ln (3 x + 4) - ln (3) - 4 ln (x^{2} - 12)

lo g_{10} (\frac{1}{5.6 \cdot 1 0 ^{- 2}})

ln (1 - 3) + ln (1 + 3)

lo g_{e} (\frac{1}{x + 1})

\frac{1}{2} ln (28)

6 ln (8) - 2 ln (3)

What is ln(((3x+4)^3)/(3(x^2-12)^4)) ?
The solution to ln(((3x+4)^3)/(3(x^2-12)^4)) is 3ln(3x+4)-ln(3)-4ln(x^2-12)