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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

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

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

Remove parentheses:

(a) = a

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

\frac{1}{8} ln (2)

ln (0.00006) - ln (0.00022)

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

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

ln (x^{2} - y) - ln (x + y) - ln (x - y)

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