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

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

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

simplify

ln 1 - 32 - ln ∣ 3 ∣

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

Decimal Notation

0.07777 \dots

Solution steps

ln 1 - 32 - ln ∣ 3 ∣

Apply log rule:

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

ln 1 - 32 - ln ∣ 3 ∣ = ln (\frac{1 - 3 2}{∣ 3 ∣})

= ln (\frac{1 - 3 2}{∣ 3 ∣})

\frac{1 - 3 2}{∣ 3 ∣} = \frac{- 1 + 3 2}{3}

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

ln (\frac{( x ^{2} + 1 ) ^{5}}{( 1 - x ) ^{\frac{1}{2}}})

6 - lo g_{10} (\frac{0.035}{0.1})

- lo g_{10} (7.57 \cdot 1 0^{- 3})

\frac{1}{0.81 \cdot 1 0 ^{- 4}} ln (\frac{1.04}{0.03})

ln (\frac{( s - a )}{s - b})

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