What is ln((3+1)/(3-1)) ?

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

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simplify ln((3+1)/(3-1))

simplify

ln (\frac{3 + 1}{3 - 1})

ln (2)

Decimal Notation

0.69314 \dots

Solution steps

ln (\frac{3 + 1}{3 - 1})

Apply log rule:

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

ln (\frac{3 + 1}{3 - 1}) = ln (3 + 1) - ln (3 - 1)

= ln (3 + 1) - ln (3 - 1)

Add the numbers:

3 + 1 = 4

= ln (4) - ln (3 - 1)

Subtract the numbers:

3 - 1 = 2

= ln (4) - ln (2)

ln (4) = 2 ln (2)

= 2 ln (2) - ln (2)

Add similar elements:

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

= ln (2)

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