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

The solution to 2ln(2+sqrt(3))-2ln(2-sqrt(3)) is ln(97+56sqrt(3))

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

simplify

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

ln (97 + 563)

Decimal Notation

5.26783 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

\frac{( 2 + 3 ) ^{2}}{( 2 - 3 ) ^{2}} = 97 + 563

= ln (97 + 563)

ln (\frac{x ^{3.9644} e ^{- x}}{3.9644 !})

ln (\frac{( l + s )}{s})

ln (\frac{55}{50})

ln (\frac{99.6}{8.2})

60 e^{\frac{l n ( 48 )}{l n ( 60 ) 3}}

What is 2ln(2+sqrt(3))-2ln(2-sqrt(3)) ?
The solution to 2ln(2+sqrt(3))-2ln(2-sqrt(3)) is ln(97+56sqrt(3))