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

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

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simplify ln(x+1)-2ln(2x^2+2)

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

5 ln (x - 4) - ln (x^{2} - 9 x + 20) + 2 ln (x - 5)

lo g_{2} (a c) - \frac{1}{4} lo g_{8} (b)

ln (e^{5} x^{- 2})

lo g_{10} (x^{e} e^{x})

2 + lo g_{10} (\frac{8}{0.1})

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