What is ln((1^4)/((1+1)^4)) ?

The solution to ln((1^4)/((1+1)^4)) is -4ln(2)

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simplify ln((1^4)/((1+1)^4))

simplify

ln (\frac{1 ^{4}}{( 1 + 1 ) ^{4}})

- 4 ln (2)

Decimal Notation

- 2.77258 \dots

Solution steps

ln (\frac{1 ^{4}}{( 1 + 1 ) ^{4}})

Apply log rule:

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

ln (\frac{1 ^{4}}{( 1 + 1 ) ^{4}}) = ln (1^{4}) - ln ((1 + 1)^{4})

= ln (1^{4}) - ln ((1 + 1)^{4})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (1^{4}) = 4 ln (1)

= 4 ln (1) - ln ((1 + 1)^{4})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln ((1 + 1)^{4}) = 4 ln (1 + 1)

= 4 ln (1) - 4 ln (1 + 1)

4 ln (1) = 0

4 ln (1 + 1) = 4 ln (2)

= 0 - 4 ln (2)

0 - 4 ln (2) = - 4 ln (2)

= - 4 ln (2)

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