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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

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

ln (\frac{9}{4})

lo g_{a} (\frac{( x + y ) ^{3}}{( x - y ) ^{2}})

2 ln (x) + 5 ln (2) - ln (8)

7 ln (x) + 2 ln (3) - 5 ln (y)

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