What is (-ln(2))ln^2((-ln(2))/2) ?

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

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simplify (-ln(2))ln^2((-ln(2))/2)

simplify

(- ln (2)) ln^{2} (\frac{- ln ( 2 )}{2})

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

Solution steps

(- ln (2)) ln^{2} (\frac{- ln ( 2 )}{2})

Apply log rule:

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

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

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

Remove parentheses:

(- a) = - a

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

Apply the distributive law:

a (b - c) = ab - a c

a = - ln (2), b = ln^{2} (- ln (2)), c = ln^{2} (2)

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

Apply minus-plus rules

- (- a) = a

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

ln^{2} (2) ln (2) = ln^{3} (2)

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

lo g_{2} (\frac{x}{8})

lo g_{2} (\frac{32}{x y ^{2}})

lo g_{10} (\frac{x + 7}{x - 1})

3 ln (x) + 6 ln (y) - 5 ln (z)

2 lo g_{3} (x) + lo g_{3} (y) - \frac{1}{2} lo g_{3} (z)

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