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

The solution to 3ln(x)+1/3 ln(x+2) is ln(x^3(x+2)^{1/3})

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simplify 3ln(x)+1/3 ln(x+2)

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

ln (x^{3} yz)

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

- lo g_{10} (4.18 \cdot 1 0^{- 3})

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

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

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