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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

x x^{2} : x^{3}

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

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

- \frac{3 ln ( \frac{2}{3} )}{ln ( \frac{9}{4} ) - ln ( \frac{2}{3} )}

\frac{- ln ( \frac{7}{2} ) + 2 ln ( 10 )}{ln ( 10 )}

ln (x e^{- x})

(ln^{2} (x) + ln (x) - 2) (lo g_{5} (x) - 2)

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