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

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

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simplify ln((4x^4)/(x^3+3))

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

ln (4) = 2 ln (2)

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

- ln (\frac{x}{3})

15 lo g_{5} (a) + 3 lo g_{5} (b)

9 ln (x + 9) - 8 ln (x)

ln ((sin (x))^{3})

20 \cdot lo g_{10} (\frac{x \cdot 2 π \cdot 628.32}{( 10 \cdot 0.02 )})

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