What is ln|sqrt(5)+2|-ln|sqrt(5)-2| ?

The solution to ln|sqrt(5)+2|-ln|sqrt(5)-2| is ln(9+4sqrt(5))

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simplify ln|sqrt(5)+2|-ln|sqrt(5)-2|

simplify

ln 5 + 2 - ln 5 - 2

ln (9 + 45)

Decimal Notation

2.88727 \dots

Solution steps

ln 5 + 2 - ln 5 - 2

Apply log rule:

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

ln 5 + 2 - ln 5 - 2 = ln (\frac{2 + 5}{5 - 2})

= ln (\frac{5 + 2}{5 - 2})

\frac{5 + 2}{5 - 2} = 9 + 45

= ln (9 + 45)

2 ln (3) + 2 ln (6) + 2 ln (2) + 2 ln (3) + 2 ln (x)

ln (\frac{( e ^{x} + e ^{- x} )}{2})

ln (\frac{3}{4}) \cdot \frac{3}{4} + ln (\frac{1}{4}) \cdot \frac{1}{4}

0.3 \cdot ln (x) - ln (x + 3)

- lo g_{10} (7.98 \cdot 1 0^{- 2})

What is ln|sqrt(5)+2|-ln|sqrt(5)-2| ?
The solution to ln|sqrt(5)+2|-ln|sqrt(5)-2| is ln(9+4sqrt(5))