What is ln|2+sqrt(3)|-ln|sqrt(2)+1| ?

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

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simplify ln|2+sqrt(3)|-ln|sqrt(2)+1|

simplify

ln 2 + 3 - ln 2 + 1

ln ((2 + 3) (2 - 1))

Decimal Notation

0.43558 \dots

Solution steps

ln 2 + 3 - ln 2 + 1

Apply log rule:

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

ln 2 + 3 - ln 2 + 1 = ln (\frac{2 + 3}{1 + 2})

= ln (\frac{2 + 3}{2 + 1})

\frac{2 + 3}{2 + 1} = (2 + 3) (2 - 1)

= ln ((2 + 3) (2 - 1))

lo g_{10} (\frac{x ^{2}}{z})

ln (\frac{x ^{9} x ^{2} + 3}{( x + 3 ) ^{6}})

ln (x) - ln (x - 4) + \frac{1}{2} ln (x + 1)

\frac{1}{2} ln (x) + 6 ln (y) - 9 ln (z)

lo g_{10} (\frac{- 5 ^{7} 2 ^{5}}{- 1 0 ^{8}})

What is ln|2+sqrt(3)|-ln|sqrt(2)+1| ?
The solution to ln|2+sqrt(3)|-ln|sqrt(2)+1| is ln((2+sqrt(3))(sqrt(2)-1))