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)

lo g_{10} (4 \frac{4 ^{a}}{( a - 4 ) ( 3 a - 4 )})

lo g_{3} (80) \cdot \frac{4}{5}

lo g_{10} (x) + \frac{1}{2} lo g_{10} (y)

lo g_{2} ((2 x - 2)^{2}) - 4 lo g_{2} (1 - x)

f (x) = - lo g_{10} (2.5 x \cdot 1 0^{- 7})

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)