What is 1/3 [ln(x+3)+2ln(x^3+2x)] ?

The solution to 1/3 [ln(x+3)+2ln(x^3+2x)] is 1/3 ln((x+3)(x^3+2x)^2)

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simplify 1/3 [ln(x+3)+2ln(x^3+2x)]

simplify

\frac{1}{3} [ln (x + 3) + 2 ln (x^{3} + 2 x)]

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

Solution steps

\frac{1}{3} [ln (x + 3) + 2 ln (x^{3} + 2 x)]

Apply log rule:

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

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

= \frac{1}{3} [ln (x + 3) + ln ((x^{3} + 2 x)^{2})]

Apply log rule:

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

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

= \frac{1}{3} [ln ((x + 3) (x^{3} + 2 x)^{2})]

Remove parentheses:

(a) = a

= \frac{1}{3} ln ((x + 3) (x^{3} + 2 x)^{2})

\frac{ln ( 4.1 ) - ln ( 3.9 )}{4 \cdot 0.1}

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

ln (\frac{10}{620.9 9 ^{2}})

\frac{9}{2} ln (2)

\frac{1}{2} ln (u) - \frac{1}{2} ln (u - 1)

What is 1/3 [ln(x+3)+2ln(x^3+2x)] ?
The solution to 1/3 [ln(x+3)+2ln(x^3+2x)] is 1/3 ln((x+3)(x^3+2x)^2)