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

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

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simplify ln((x^2sqrt(3x-2))/((x+1)^2))

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= 2 ln (x) + ln (3 x - 2) - 2 ln (x + 1)

ln (x^{7} (x + 9)^{5} (x^{2} + 9)^{7})

ln (t) + 7 ln (r) - 6 ln (t)

2 (1 - ln (3) + ln (2))

lo g_{2} (\frac{n}{3 ^{i}})

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

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