What is 2*ln(-2)-2*ln(2) ?

The solution to 2*ln(-2)-2*ln(2) is 0

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simplify 2ln(-2)-2ln(2)

simplify

2 \cdot ln (- 2) - 2 \cdot ln (2)

0

Solution steps

2 ln (- 2) - 2 ln (2)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

\frac{( - 2 ) ^{2}}{2 ^{2}} = 1

= ln (1)

Apply log rule:

lo g_{a} (1) = 0

= 0

ln (\frac{4}{10000})

\frac{1}{2} ln (9 t^{10}) - ln (3)

5 ln (x^{\frac{1}{3}}) + ln (9 x)

5 ln (2) - 5 ln (- 2)

ln ((e + 1) (e - 1)) - 1