What is 2-3ln(-2)-4+3ln(-4) ?

The solution to 2-3ln(-2)-4+3ln(-4) is 3ln(2)-2

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simplify 2-3ln(-2)-4+3ln(-4)

simplify

2 - 3 ln (- 2) - 4 + 3 ln (- 4)

3 ln (2) - 2

Decimal Notation

0.07944 \dots

Solution steps

2 - 3 ln (- 2) - 4 + 3 ln (- 4)

Apply log rule:

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

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

= 2 - ln ((- 2)^{3}) - 4 + 3 ln (- 4)

Apply log rule:

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

3 ln (- 4) = ln ((- 4)^{3})

= 2 - ln ((- 2)^{3}) - 4 + ln ((- 4)^{3})

Apply log rule:

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

ln ((- 4)^{3}) - ln ((- 2)^{3}) = ln (\frac{( - 4 ) ^{3}}{( - 2 ) ^{3}})

= 2 + ln (\frac{( - 4 ) ^{3}}{( - 2 ) ^{3}}) - 4

\frac{( - 4 ) ^{3}}{( - 2 ) ^{3}} = 8

= 2 + ln (8) - 4

Subtract the numbers:

2 - 4 = - 2

= ln (8) - 2

ln (8) = 3 ln (2)

= 3 ln (2) - 2

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

- \frac{5 ln ( 2 )}{ln ( 3 )}

7089.884206 \cdot ln (\frac{x ^{2}}{4.5 \cdot 1 0 ^{8}})

ln (\frac{8 u + 3}{8 u - 3})

e^{x + l n (x)} + ln (\frac{1}{x ^{3}})