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

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

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

simplify

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

2 ln (2) + 2 ln (x) - 3 ln (x + 3)

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

= ln (4) + 2 ln (x) - 3 ln (x + 3)

ln (4) = 2 ln (2)

= 2 ln (2) + 2 ln (x) - 3 ln (x + 3)

ln (\frac{1 - x}{3})

lo g_{a} (a) b + lo g_{a} (\frac{a}{b})

lo g_{7} (\frac{h - 3}{49})

\frac{1}{2} ln (x) + 3 ln (y) - 2 ln (x)

lo g_{4} (u) + 6 lo g_{4} (v) + 3 lo g_{4} (w)

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