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

The solution to 2(ln(sqrt(2)+1)-2ln(sqrt(2)-1)) is 2ln(5sqrt(2)+7)

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

simplify

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

2 ln (52 + 7)

Decimal Notation

5.28824 \dots

Solution steps

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

Apply log rule:

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

2 ln (2 - 1) = ln ((2 - 1)^{2})

= 2 (ln (1 + 2) - ln ((2 - 1)^{2}))

Apply log rule:

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

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

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

\frac{2 + 1}{( 2 - 1 ) ^{2}} = 52 + 7

= 2 ln (52 + 7)

lo g_{9} ((\frac{x}{y})^{4})

- lo g_{10} (5.7 (1 0^{- 8}))

- lo g_{10} (9.49 \cdot 1 0^{- 1})

lo g_{10} (\frac{2 x ^{5}}{( 7 + x ) ^{4}})

lo g_{3} (x \cdot sin (x))

What is 2(ln(sqrt(2)+1)-2ln(sqrt(2)-1)) ?
The solution to 2(ln(sqrt(2)+1)-2ln(sqrt(2)-1)) is 2ln(5sqrt(2)+7)