What is 1/2 [ln(x)+2ln(x+1)]+3ln(x-5) ?

The solution to 1/2 [ln(x)+2ln(x+1)]+3ln(x-5) is 1/2 ln(x(x+1)^2)+3ln(x-5)

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simplify 1/2 [ln(x)+2ln(x+1)]+3ln(x-5)

simplify

\frac{1}{2} [ln (x) + 2 ln (x + 1)] + 3 ln (x - 5)

\frac{1}{2} ln (x (x + 1)^{2}) + 3 ln (x - 5)

Solution steps

\frac{1}{2} [ln (x) + 2 ln (x + 1)] + 3 ln (x - 5)

Apply log rule:

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

2 ln (x + 1) = ln ((x + 1)^{2})

= \frac{1}{2} [ln (x) + ln ((x + 1)^{2})] + 3 ln (x - 5)

Apply log rule:

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

ln (x) + ln ((x + 1)^{2}) = ln (x (x + 1)^{2})

= \frac{1}{2} [ln (x (x + 1)^{2})] + 3 ln (x - 5)

Remove parentheses:

(a) = a

= \frac{1}{2} ln (x (x + 1)^{2}) + 3 ln (x - 5)

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

\frac{4}{3 ln ( 3 )} + \frac{10}{3} - \frac{2}{ln ( 2 )}

2 \cdot ln (x) + \frac{1}{3} \cdot ln (x - 2) - 5 \cdot ln (2 x + 3)

ln (3) - ln (3 - x)

27 lo g_{10} (x) + lo g_{10} (y) - 12 lo g_{10} (z)

What is 1/2 [ln(x)+2ln(x+1)]+3ln(x-5) ?
The solution to 1/2 [ln(x)+2ln(x+1)]+3ln(x-5) is 1/2 ln(x(x+1)^2)+3ln(x-5)