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

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

Popular >

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

simplify

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

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

Solution steps

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

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

Apply log rule:

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

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

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

Remove parentheses:

(a) = a

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

ln ((e^{3}) \cdot (x^{3}) \cdot (y^{4}))

\frac{5}{4} ln (x) - \frac{7}{2 x} - \frac{5}{4} ln (x + 2) + C

lo g_{10} ((tan (x))^{\circ}) 2 x

2 lo g_{10} (x) - 5 lo g_{10} (x - 1)

- lo g_{10} (2.7 \cdot 1 0^{- 7})

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